Question

The parent function f(x) = x3 is represented by graph A. Graph A is transformed to get graph B and graph C. Write the functions represented by graph B and graph C. Graph B represents the function g(x) = . Graph C represents the function h(x) = .

Answer 1

The parent function f(x) = x^3 is represented by graph A.

The graph B is shifted 2 units down

If graph is shifted down then we put negative

We subtracted 2 at the end

so the function represented by Graph B is

$f(x) = x^3 - 2$

Now we look at the graph C

The graph C is stretched vertically

In graph A we have point (1,1)

In graph C  we have point (1,2)

It means y is multiplied by 2

So the graph C is stretched vertically by 2 units

So for graph C $f(x) = 2x^3$

Answer 2

Graph B represents the function g(x)=x^3-2 Graph C represents the function h(x)=2x^3