Question

Select the correct answer from each drop-down menu.
The table represents function f, and the graph represents function g.
-2
- 1
1
2
3
4
0
х
Ax)
7
0
-5
-8
-9
-8
-5
у
A
6
4
2
g
X
.
-21
2
2
The line of symmetry for function fis
and the line of symmetry for function gis
The y-intercept of function fis
the y-intercept of function g.
Over the interval [2, 4], the average rate of change of function fis
the average rate of change of function g.

Answer 1

Answer:

Line of symmetry of f is x=2 and the line of symmetry for function g is x=1 as the graph starts repeating itself after x=1. Y intercept is the point at which x is 0, for f it is - 5 and for g it is - 6. Rate of change in interval [2,4] is given by (f(4)-f(2))/2=2 for f and for g it is, (g(4)-g(2))/2=-4

Answer 2

The true statements are:

• The line of symmetry for function f is x = 2
• The line of symmetry for function g is x = 1
• The y-intercept of function f is -5
• The y-intercept of function g is -6
• Over the interval [2, 4], the average rate of change of function f is half the average rate of change of function g.

Line of Symmetry

This is the point where the function is divided into equal halves.

From the figure, the table and graph are divided at points x = 2, and x = 1.

So, the line of symmetry for function f is x = 2 and the line of symmetry for function g is x = 1

Y-Intercept

This is the point where the function has an x value of 0

From the figure, the y values when x = 0 are -5 and -6

So, the y-intercept of function f is -5 and the y-intercept of function g is -6

Average rate of change

This is calculated as:

$m = \frac{y_2 - y_1}{x_2 -x_1}$

For function f, we have:

$m = \frac{-5 + 9}{4-2}$

$m = \frac{4}{2}$

$m = 2$

For function g, we have:

$m = \frac{2+ 6}{4-2}$

$m = \frac{8}{2}$

$m = 4$

By comparison,

$m_f = 0.5 \times m_g$

Hence, over the interval [2, 4], the average rate of change of function f is half the average rate of change of function g.

Read more about functions and graphs at:

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