Question

use transformations of \\(f(x) = \sqrt3{x}\\) to graph the following function.

\\h(x) = -\sqrt3{x+4}\\

select all the transformations that are needed to graph the given function using \\(f(x) = \sqrt3{x}\\).

a. shift the graph 4 units to the right.
b. stretch the graph horizontally by a factor of 4.
c. shrink the graph horizontally by a factor of 4.
d. stretch the graph vertically by a factor of 4.
e. shift the graph 4 units up.
f. reflect the graph about the y-axis.
g. shift the graph 4 units to the left.
h. shrink the graph vertically by a factor of 4.
i. shift the graph 4 units down.
j. reflect the graph about the x-axis.

Explanation:

Identify the parent function and the transformed function

$$
LATEXBLOCK0
$$

Analyze the horizontal transformation

$$
LATEXBLOCK1
$$

Analyze the vertical transformation

$$
LATEXBLOCK2
$$

Answer:

• A. Shift the graph 4 units to the right.
• B. Stretch the graph horizontally by a factor of 4.
• C. Shrink the graph horizontally by a factor of 4.
• D. Stretch the graph vertically by a factor of 4.
• E. Shift the graph 4 units up.
• F. Reflect the graph about the y-axis.
• G. Shift the graph 4 units to the left. (Correct answer)
• H. Shrink the graph vertically by a factor of 4.
• I. Shift the graph 4 units down.
• J. Reflect the graph about the x-axis. (Correct answer)