Question

consider the parent function f(x)=x^2. a. graph y=f(x). b. write an equation for f(1/2x). Then sketch a graph of y=f(1/2x) and describe the transformation. c.write an equation for f(3x). Then sketch a graph of y=f(3x) and describe the transformation.

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

f(x)=x²

f(1/2x) = ?

graph of y=f(1/2x) = ?

Step 02:

b. f(1/2x)

x ===> 1/2x

`f\text{ (1/2 x) = (}(1)/(2)x)^2=(1)/(4)x^2`

Step 03:

c. Graph:

We give values to x, and we obtain the values of y.

f(x) = 1/4 x²

e.g.

if x = 4

y = 1/4 (4)² = 1/4 * 16 = 4

That is the solution for b. and c.