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

Question

asked Sep 23, 2021 137k views

1 Answer

Seok · Answer 1 · 2021-09-26T17:07:45+0000

Answer:

A)
y=-5x-4

B)
y=-5x+4

C)
y=(x-4)/(5)

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)=(x-4)/(5)

And we're done :)