Suppose f(x) = 3x^2 − 5 represents a transformation of the function shown on the graph. Which statement BEST describes the transformation?

Question

Suppose f(x) = 3x^2 − 5 represents a transformation of the function shown on the graph. Which statement BEST describes the transformation?

Responses

1. 
   
2. A
3. The graph is stretched by a factor of 3 with respect to the x-axis and shifted right 5 units.
4. B
5. The graph is stretched by a factor of 3 with respect to the x-axis and shifted down 5 units.
6. C
7. The graph is stretched by a factor of 3 with respect to the y-axis and shifted down 5 units.
8. D
9. The graph is stretched by a factor of 3 with respect to the y-axis and shifted up 5 units.

Answer 1

3 is not inside what's being done to x. That would be (3x)^2 - 5. 3*x^2 stretches the graph vertically (y-axis) by a factor of 3. The -5 does shift it down.

Try some values:

x=1. 1, -2 (that's stretched vertically by 3 to 3, then shifted down 5 to -2)

x=2. 4, 7 (stretched vertically by 3 to 12, then shifted down 5 to 7.)

The correct answer is C.

Graph them on Desmos to see.

Answer 2

Well, as you indicated, it's B

f(x) = 3x^2 − 5

is a transformation of x^2, by stretching by a factor of 3 (3 x^2)

And shifted down by -5