Question

What is the equation when y=5x+4 is reflected over the x-axis, y-axis & y=x?

Answer 1

Answer:

A) $y=-5x-4$

B) $y=-5x+4$

C) $y=\frac{x-4}{5}$

Step-by-step explanation:

So we have the equation:

$y=5x+4$

Let's write this in function notation. Thus:

$y=f(x)=5x+4$

A)

To flip a function over the x-axis, multiply the function by -1. Thus:

$f(x)=5x+4\\-(f(x))=-(5x+4)$

Simplify:

$-f(x)=-5x-4$

B) To flip a function over the y-axis, change the variable x to -x. Thus:

$f(x)=5x+4\\f(-x)=5(-x)+4$

Simplify:

$f(-x)=-5x+4$

C) A reflection over the line y=x is synonymous with finding the inverse of the function.

To find the inverse, switch x and f(x) and solve for f(x):

$f(x)=5x+4$

Switch:

$x=5f^{-1}(x)+4$

Subtract 4 from both sides:

$x-4=5f^{-1}(x)$

Divide both sides by 5:

$f^{-1}(x)=\frac{x-4}{5}$

And we're done :)