Question

Write the equation for f(x) and g(x). Then identify the reflection that transforms the graph of f(x) to the graph of g(x).

Answer 1

Given the figure of the functions f(x) and g(x)

The graph of the function is the shown lines

The equation of f(x):

As shown the line of f(x) passes through the points: (-2, 0) and (0, -1)

The slope of the line will be:

$slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-0}{0-(-2)}=\frac{-1}{2}$

The y-intercept = -1

so, the equation of f(x) =

$f(x)=-\frac{1}{2}x-1$

The equation of g(x):

As shown the line of g(x) passes through the points: (-2, 0) and (0, 1)

The slope of the line will be:

$slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-0}{0-(-2)}=\frac{1}{2}$

The y-intercept = 1

So, the equation of g(x) will be:

$g(x)=\frac{1}{2}x+1$

Identify the reflection that transforms the graph of f(x) to the graph of g(x).

As shown, the functions are symmetric around the x-axis

And as we can see for the same value of x: g(x) = -f(x)

So, the type of transformation is: Reflection over the x-axis