Question

The function f(x) = –2/7(5/3)^x is reflected over the y-axis to create g(x). Which points represent ordered pairs on g(x)? Check all that apply. (–7, –10.206) (–2.5, –4.474) (0, –1.773) (0.5, –0.221) (4, –0.017) (9, –0.003)

Answer 1

Given:
$f(x)=- \frac{2}{7} ( \frac{5}{3} )^{x}$

We are given ordered pairs of values for g(x) whose x-values are
-7, -2.5, 0, 0.5, 4, and 9.

After reflection across the x-axis, f(x) should have negative x-values, but the same y-values.
Use the calculator to create a table of f(x), with x-values of
7, 2.5, 0, -0.5, -4, and -9. 

x:               7        2.5            0      -0.5         -4          -9
f(x):  -10.206   -1.025  -0.286   -0.221  -0.037  -0.003

The corresponding values for g(x) will match f(x), but the x-values will be multiplied by -1.

Answer:
Of the given answers, only these are correct:
(-7, -10.206)
(0.5, -0.221)
(9, 0.003)

Answer 2

Answer:

• (–7, –10.206)  

• (0.5, –0.221)

• (9, –0.003)

Step-by-step explanation:

When we reflect the graph on the y axis, we will have the opposite values for x ---> what was once x is now -x. And the values for y remain the same.

So we can represent the new function g(x) as:

$g(x) =-2/7(\frac{5}{3})^{-x}$

We change the x of the original function f(x) by -x due to the reflection on the y axis.

Now we verify that the points given are of the function g(x)

• (–7, –10.206)  

$x = -7$

$g(-7) =-\frac{2}{7} (\frac{5}{3})^{-(-7)}=-\frac{2}{7} (\frac{5}{3})^{7} = -10.206$

The points for y given by the option and by the function match, so it is an ordered pair of g(x)

• (–2.5, –4.474)

$x = -2.5$

$g(-2.5) =-\frac{2}{7} (\frac{5}{3})^{-(-2.5)}=-\frac{2}{7} (\frac{5}{3})^{2.5} = -1.025$

The points for y given by the option and by the function do NOT match, so it is not an ordered pair of g(x)

• (0, –1.773)

$x = 0$

$g(0) =-\frac{2}{7} (\frac{5}{3})^{-0}=-\frac{2}{7} (\frac{5}{3})^0} = -0.286$

The points for y given by the option and by the function do NOT match, so it is not an ordered pair of g(x)

• (0.5, –0.221)

$x= 0.5$

$g(0.5) =-\frac{2}{7} (\frac{5}{3})^{-0.5}= -0.221$

The points for y given by the option and by the function match, so it is an ordered pair of g(x)

• (4, –0.017)

$x = 4$

$g(4) =-\frac{2}{7} (\frac{5}{3})^{-4}= -0.037$

The points for y given by the option and by the function do NOT match, so it is not an ordered pair of g(x)

• (9, –0.003)

$x= 9$

$g(9) =-\frac{2}{7} (\frac{5}{3})^{-9}= -0.003$

The points for y given by the option and by the function match, so it is an ordered pair of g(x)

In summary, the points that are part of the function g(x) are:

• (–7, –10.206)  

• (0.5, –0.221)

• (9, –0.003)