Question

Describe how the graph of g(x) is related to the graph of f(x) = x3

g(x) = (x+2)3 (power of 3)

g(x) = -1/2x3 (power of 3)

g(x) = (4x)3 (power of 3) + 3

Answer 1

(a)

f(x) is shifted left side by 2 units

(b)

f(x) is vertically compress by 2 units

(c)

f(x) is horizontally compress by 4 units

f(x) is vertically shifted upside by 3 units

Explanation:

we are given

parent function as

`f(x)=x^3`

(a)

we have

`g(x)=(x+2)^3`

we can see that in place x , we have x+2

It means that f(x) is shifted left side by 2 units

So, f(x) is shifted left side by 2 units

(b)

`g(x)=-(1)/(2)x^3`

we can see that -1/2 is multiplied

Since, negative sign is multiplied to y-value

so, f(x) is reflected about x-axis

and 1/2 is multiplied to y-value

so, f(x) is vertically compress by 2 units

(c)

we are given

`g(x)=(4x)^3+3`

we can see that in place x , we have 4x

so, f(x) is horizontally compress by 4 units

and 3 is added to y-value

so, f(x) is vertically shifted upside by 3 units