Consider the function given by the graph. What are
these values?
fl-2) =
10) =
f(4) =
Answers
Answer:
f(-2) = 2
f(0) = 4
f(4) = -1
Step-by-step explanation:
Given the graph of a piecewise function:
[tex]\displaystyle\mathsf{f(x) = \left \{ {{x\:+\:4\quad if\:\:x\leq \:0} \atop {-\frac{1}{2}x\:+\:1\quad if\:\:x\: >\:0}} \right.}\\[/tex]
Side note:
I used the method of finding the linear equations in slope-intercept form to establish the piecewise function. First, I solved for the slope by choosing two points in each defined interval. Then, I plugged in the y-intercepts of each interval, for f(x) = x + 4: the y-intercept is (0, 4) where b = 4; for f(x) = -½x + 1, the y-intercept is (0, 1) where b = 1.
Explanation:There are two methods for determining the range values of the given domain values.
Method 1: The first method is using the graph to find the corresponding range values of the given domain {-2, 0, 4}.
Method 2: Alternatively, we could use the rules provided by the piecewise function in evaluating the following domain values. This post will use the second method (using the piecewise function) to evaluate the input values.
Regardless of the method used, the results will remain the same.
f(-2)Since the input value is x = -2, then we must use the function, f(x) = x + 4:
f(x) = x + 4
f(-2) = -2 + 4
f(-2) = 2
Therefore, the range value given the domain, x = -2 is 2, or simply: f(-2) = 2.
f(0)
Given the input value is x = 0, then we must also use the function, f(x) = x + 4:
f(x) = x + 4
f(0) = 0 + 4
f(0) = 4
Therefore, the range value given the domain, x = 0 is 4, or f(0) = 4.
f(4)
Since the input value is x = 4, then we must use the function, f(x) = -½x + 1:
f(x) = -½x + 1
f(4) = -½(4) + 1
f(4) = -2 + 1
f(4) = -1
Therefore, the range value given the domain, x = 4 is -1, or f(4) = -1.
Related Questions
Janine opens a savings account with a deposit of $720. The account pays 1.4% interest, compounded daily. What is the first day's interest? Round to the nearest cent.
Answers
Answer:
The interest is $0.03
Step-by-step explanation:
($720*0.014)/365
The first day's interest will be $10.15 if Janine opens a savings account with a deposit of $720. The account pays 1.4% interest, compounded daily.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
It is given that:
Janine opens a savings account with a deposit of $720. The account pays 1.4% interest, compounded daily.
P =$720
r = 1.4% = 0.014
n = 365
t = 1 day
[tex]\rm A = 720(1+\dfrac{0.014}{365})^{365\times1}[/tex]
After solving:
A = $730.15
The interest I = A - P
I = $730.15 - 720
I = $10.15
Thus, the first day's interest will be $10.15 if Janine opens a savings account with a deposit of $720. The account pays 1.4% interest, compounded daily.
Learn more about the compound interest here:
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Please help! Will mark brainliest.
Convert into an exponential expression.
Answers
Answer:
Step-by-step explanation:
5√7²=5√49=9.8
The price of trail mix at a health food store is
$7.50 per pound. At that rate, what is the total
cost of three 8-ounce bags of trail mix?
Answers
Answer:
$3.75 every 8 oz bags.
Step-by-step explanation:
7.5 divided by 2 to get 3.75. 1 LB is equal to 16 oz so 8 is half of 16.
3 (x-1)=3x-×-3-3+x+3
True or false
Answers
true
Step-by-step explanation:
Answer:
3x-3
Step-by-step explanation:
So false if you Multiply
I don’t know what I got wrong on this problem. Can someone please help me?
Answers
Answer:
x is equal to the length of that side of the triangle, the x is written on (the distance between the log ride and the pirate ship). You can visually see that both of the long sides of that triangle are equal. See how they look the same? The other side of that triangle (the distance between the Big Top Tent and the Pirate Ship) has a given length written, it says "25 m." So the x side, which is equal is also 25 m. The value of x is 25 m.
Step-by-step explanation:
The school that Michael goes to is selling tickets to a dance. On the first day of ticket sales the school sold 3 staff tickets and 1 student ticket for a total of $38. The school took in $52 on the second day by selling 3 staff tickets and 2 student tickets. Find the price of a staff ticket and the price of a student ticket.
Answers
The price of a staff ticket and the price of a student ticket is $8 and $14
Given:
Day 1:
Number of staff tickets sold = 3
Number of students tickets sold = 1
Total revenue day 1 = $38
Day 2:
Number of staff tickets sold = 3
Number of students tickets sold = 2
Total revenue day 2 = $52
let
cost of staff tickets = x
cost of students tickets = y
The equation:
3x + y = 38 (1)
3x + y = 38 (1)3x + 2y = 52 (2)
subtract (1) from (2)
2y - y = 52 - 38
y = 14
substitute y = 14 into (1)
3x + y = 38 (1)
3x + 14 = 38
3x = 38 - 14
3x = 24
x = 24/3
x = 8
Therefore,
cost of staff tickets = x
= $8
cost of students tickets = y
= $14
Read more:
https://brainly.com/question/22940808
Use the simple interest formula 1=prt find the amount that needs to be invested at 7%per year for 12 years in order to earn 2500$in interest
Answers
A cab company charges a $3 boarding rate in addition to its meter which is $2 for every mile. What is the equation of the line that represents this cab company's rate?
Answers
well im guessing it the average highway speed 60 mph so it is $7
Apologize If i keep spamming this question, I just really need help
Answers
Answer:
C , 18
Step-by-step explanation:
Answer:
The sum of the exterior angles of a polygon is always 360°.
Therefore,
[tex]x+2x+3x+5x+9x=360[/tex]
[tex]20x=360[/tex]
Divide both sides by 20:
[tex]\frac{20x}{20}=\frac{360}{20}[/tex]
[tex]x=18[/tex]
each ball has a diameter of 60mm
which has the smallest surface area?
Answers
Mary earns a weekly base salary of $180. She also receives $25 per item sold. This week
she receives a salary of $530. How many items did she sell?
Answers
Answer:
She sold 14 items
Step-by-step explanation:
530 - 180 = 350
350 / 25 = 14
The radius of a cycle wheel is 35 cm. Find the number of turns required to cover a distance of 1540 m
Answers
Answer:
1 I think can you make sure?
Factor x3 – 7x2 – 5x + 35 by grouping. What is the resulting expression?
Answers
Answer:
(x-7)(x^2-5)
Step-by-step explanation:
Owen's score in a card game is 6
points away from zero. If David's score
is the opposite of Owen's and is a
positive value, what is David's score?
Answers
Answer:
aaa is easy you can pitch the ball
Owen's score will be (-6) and David's score will be opposite to that of Owen's score and a positive value, which will be (+6).
What is absolute value of a number?The absolute value of a number is the magnitude of number. Absolute value describes the distance from zero that a number is on the number line, without considering direction.
We have Owen's score in a card game is 6 points away from zero. David's score is the opposite of Owen's and is a positive value.
For a number [x], such that [x] < 0, the absolute value would be -
v[a] = -x
A number cannot be negative and positive at the same time, therefore, Owens score is 6 points away from 0, but in the negative direction of number line. So, Owen's score will be (-6) and David's score will be opposite to that of Owen's score and a positive value, which will be (+6).
Therefore, Owen's score will be (-6) and David's score will be opposite to that of Owen's score and a positive value, which will be (+6).
To solve more questions on number line, visit the link below-
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HELP!!! Worth 50 points
Answers
Answer:
with what
Step-by-step explanation:
I am confused there is no question at all showing
Answer:
Answer:
The correct answer is C - 7.8 < 7 5/6 < 7.9
Step-by-step explanation:
First, convert 7 5/6 to decimal form --> 7.83.
If you don't know how to convert, think about what 5/6 is equal to and put it in decimal form. Add your decimal to the whole number, and there is your answer.
7.83 is in between 7.8 and 7.9, so it must be the answer.
I hope this helps!
Step-by-step explanation:
Write in point slope form the equation for the line that goes through the point (-1,-6) and has a slope of 16
Answers
Answer:
y+6 = 16 (x+1)
Step-by-step explanation:
Point slope form of an equation is
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
y- -6 = 16 (x- -1)
y+6 = 16 (x+1)
What Is the Intersection of Two Sets
Answers
Answer:
the set of elements that are common to each of the given sets
Step-by-step explanation:
Difference between 42.4 and 3.74
Answers
Answer:
38.66
Step-by-step explanation:
(2.5×10^6)–(2.3×10^6)
Answers
Answer:
2×[tex]10^{5}[/tex]
aka 200000
Step-by-step explanation:
Can someone help me pleaseeeeeee :( no links pleaseee
Answers
a) Keith's car will have less gas.
Locate the point in which miles driven = 90 (Between 60 and 120)
Since Keith's line is lower than Carmen, he has less gas.
We can also find the difference: 11 - 10 = 1.
It will have 1 less gallon.
b) Look at the point in which both lines meet. This means that they have the same amount of gallons remaining (8) at 180 miles driven.
Before 180 miles, Keith's car will always have less car remaining.
The price of a t-shirt is $15. If you buy more than 4 shirts, you will get 15% discount. How much do you have to pay (before tax) if you buy 8 shirts?
Answers
Compare the fractions using the LCM.
1\7,2\3
Enter the correct inequality in the box.
Answers
Answer:
42
Step-by-step explanation:
1*3=3
it becomes 2,3 and 7
you will get the answer as 42
Evaluate the expression-3 x + 4 when x = 2.
Answers
Answer:
-2
Step-by-step explanation:
-3x + 4
-3(2) + 4
-6 + 4
-2
Substitute in 2 for x, and solve.
please help me with this
Answers
Just a very quick question for any people willing to answer this question.
4 less than the number n is -15.
(Please type equation and solution!)
Answers
Answer:
n=-11
Step-by-step explanation:
n-4=-15
n-4+4=-15+4
n=-11
Each side of an equilateral triangle has length x+3 and each side of a square has length 4x-2. Write an expression for the sum of their perimeters.
Please help me!!
Answers
Answer:
square: 16x-8
triangle: 3x+9
Step-by-step explanation:
Squares have 4 equal sides. Equilateral triangles have 3 equal sides.
Multiply the length of one side by the total number of sides for each shape to find the perimeter. Then combine like terms.
Answer:
square: 16x-8
triangle: 3x+9
Step-by-step explanation:
Colin predicted whether he got answers right or wrong in his 50 question exam.
He identified the 12 questions he thought he got wrong.
It turns out that Colin got 5 questions right that he thought he got wrong.
Colin also got a total score of 42 out of 50 in the test.
What is the percentage accuracy he had with predicting his scores?
Answers
Step-by-step explanation:
so, he predicted he had 12 questions wrong.
that would have been a score of 38.
but he got 42.
that is a difference of 42-38 = 4.
now, accuracy could have different meanings like actual score vs. predicted score, or which questions were right or wrong (for real or predicted), or only looking at the questions that were right (real vs. predicted), ...
I assume it is the first one.
so,
100% = 38 (prediction)
1% = 100%/100 = 38/100 = 0.38
how many % are these 4 questions that his prediction was off from reality ?
4 / 0.38 = 10.52631579...
so, his prediction was off by about 10.53%
if f(x)=4x+3 and g(x)=x^2-3 what is f(g(4))
Answers
[tex]\text{Given that ,}\\\\f(x) = 4x+3\\\\g(x) = x^2 -3\\\\g(4) = 4^2 - 3 = 16-3=13\\\\f (g(4)) = f(13) = 4\times 13 + 3 = 55[/tex]
A circle has radius 1 unit. What percent of its area lies outside of the circle with the same center and a radius of 1/2?
Answers
Answer:
(3/4)pi
Step-by-step explanation:
Find the areas of the two circles and then subtract the smaller from the larger:
A of circle = (pi)r^2
Case 1: r = 1 unit: A = (pi)(1) = pi
Case 2: r = 1/2 unit: A = (pi)(1/2)^2 = pi/4
The area lying outside of the smaller circle is therefore (pi) - (pi)(1/4) = (3/4)pi
the difference of 3 times a number and 2 times that same number is 80.what is the number
Answers
n = 80