Question

Compare the function with the parent function. Without graphing, what are the vertex, axis of symmetry, and transformations of the given function?

y = 8x - 21 - 7

Answer 1

The parent function is: y = x

First, here we have two types of transformations, and we could define them in a general way as:

if we start with a function f(x)

Vertical dilation/contraction: A vertical dilation/contraction of scale factor A (A is always positive) is written as:

g(x) = A*f(x)

Vertical translation:

We can write a vertical translation of A units upwards as:

g(x) = f(x) + A

And a vertical translations of A units down can be written as:

g(x) = f(x) - A.

In this case, the transformations are:

first, a dilation of scale factor 8.

Then a translation down of 21 units

then another translation down of 7 units.

y = 8*X - 21 - 7

y = 8*x - 28.

As this is a linear equation, there are no axis of symmetry, we only could have a line of symmetry along the same line y = 8*x - 28

Again, as this function is a linear equation there is no vertex.