Question

describe the transformation of the graph of the parent function (y = \sqrt{x}) for the function (y = \sqrt{x + 7} + 5).

the graph is shifted 7 units left and 5 units up.

what is the domain of (y = \sqrt{x + 7} + 5)?

• (x \ge 0)
• (x \ge 7)
• (x \ge -7)
• all real numbers

what is the range of (y = \sqrt{x + 7} + 5)?

• (y \ge -5)
• (y \ge 5)
• (y \ge -7)
• all real numbers

Explanation:

Analyze the horizontal and vertical translations

Using the Horizontal Translation and Vertical Translation knowledge points

$$
LATEXBLOCK0
$$

Determine the domain of the function

Using the Square Root Function Domain knowledge point

$$
LATEXBLOCK1
$$

Determine the range of the function

Using the Square Root Function Range knowledge point

$$
LATEXBLOCK2
$$

Answer:

Question 1

The graph is shifted 7 units left and 5 units up.

Question 2

• \(x \ge 0\)
• \(x \ge 7\)
• \(x \ge -7\) (Correct answer)
• all real numbers

Question 3

• \(y \ge -5\)
• \(y \ge 5\) (Correct answer)
• \(y \ge -7\)
• all real numbers