Question

4. The graph of h(x) = x^2 was transformed to create the graph of k(x) = -4x^2? Which of these describes the transformation from the graph of h to the graph
of k? A.) A reflection over the x-axis and a vertical
stretch
B.) A reflection over the x-axis and a vertical
compression
C.) A reflection over the y-axis and a vertical
compression
D.) A reflection over the y-axis and a vertical stretch

Answer 1

Answer:

A. A reflection over the x-axis and a vertical stretch.

Step-by-step explanation:

Let $h(x) = x^{2}$, to obtain $k(x) = -4\cdot x^{2}$, we need to use the following two operations:

(i) Vertical stretch

$g(x) = k\cdot f(x)$, $k\in \mathbb{R}^{+}$

(ii) Reflection over the x-axis

$g(x) = -f(x)$

Let prove both transformations in $h(x)$:

Step 1 - Vertical stretch ($k = 4$)

$h'(x) = 4\cdot x^{2}$

Step 2 - Reflection over the x-axis

$k(x) = -4\cdot x^{2}$

Hence, correct answer is A.