15

Question

*
1 point
Captionless Image
A
B
C
D
23
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1 point
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A
B
C
D
30
*
1 point
Captionless Image
A
B
C
D
40
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1 point
Captionless Image
A
B
C
D

15. Which table could represent a quadratic function?
A
C
x
f(x)
X
h(x)
0
3
-1
6
1
9
0
5
2
27
1
6
3
81
2
9
B
D
x
g(x)
x
j(x)
0
-2
-3
7
1
-4
-2
7
2
-6
-1
7
3
-8
0
7

23. An equation is given.
y = (x- 3)2 + 1
Which type of function does the equation represent?
cubic
B
quadratic
exponential
square root

30. A rental company charges $2 per hour to rent a bicycle. A table showing
the prices of renting one bicycle for different amounts of time is shown.
Time (hours)
Price (dollars)
1
2
2
4
3
6
Which type of function models the price for renting one bicycle as a
function of time?
increasing linear
decreasing linear
increasing exponential
D
decreasing exponential

40. The graph of y = f (x) and a table of values for an exponential function
y = g (x) are shown.
y
+
6- /
x
g(x)
4- / y = f (x)
-2
0.25
2-+
-1
0.5
-8 -6
-4 -2 9
to
x
0
1
1
2
4-
2
4
-6-
8
Which statement correctly compares the graphs of the functions?
As the values of x increase, g (x) will eventually be greater than f (x).
As the values of x increase, f (x) will eventually be greater than g (x).
The value of the y-intercept of y = f (x) is greater than the
value of the y-intercept of y = g (x).
The value of the y-intercept of y = g (x) is greater than the
value of the y-intercept of y = f (x).

Answer 1

Based on the questions you've provided, here are the answers along with brief explanations for each:

15. Which table could represent a quadratic function?

• Answer: A
  • A quadratic function forms a parabolic shape in its graph. Upon examining the outputs for the values of x, table A shows a pattern consistent with a quadratic function with outputs increasing at a non-linear rate.

23. An equation is given. y = (x - 3)² + 1. Which type of function does the equation represent?

• Answer: B (quadratic)
  • The equation is in vertex form of a quadratic function, given by \(y = a(x-h)^2 + k\), where (h,k) is the vertex of the parabola.

30. A rental company charges $2 per hour to rent a bicycle. A table showing the prices of renting one bicycle for different amounts of time is shown. Which type of function models the price for renting one bicycle as a function of time?

• Answer: A (increasing linear)
  • The relationship between time and price is linear because the price increases by a constant amount ($2 per hour), resulting in a straight line when graphed.

40. The graph of y = f (x) and a table of values for an exponential function y = g (x) are shown. Which statement correctly compares the graphs of the functions?

• Answer: As the values of x increase, g(x) will eventually be greater than f(x).
  • If g(x) is an exponential function, it will grow faster than the linear or polynomial function represented by f(x) as x increases. Exponential functions typically outpace others in growth.

If you have additional context or need clarifications for any of the answers, feel free to share!