29. how do the graphs of the functions y = f(x) and y = f(–x) relate when
f(x) = x2 ?
a. the graphs reflect each other.
b. the second graph is a horizontal shift of the first graph by x units.
c. the graphs are identical.
d. the second graph is a vertical shift of the first graph by x units.
30. write the equation of the function g(x) that translates the parent function
f(x) = x² by shifting g(x) 7 units to the left and 5 units down.
a. g(x) = (x - 7)² - 5
b. g(x) = (x + 7)² - 5
c. g(x) = (x - 5)² - 7
d. g(x) = (x + 5)² - 7

 The correct options are

(1) C. The graphs are identical.

(2) B. g(x) = (x + 7)² - 5

Step-by-step explanation:  

(1) We are to find the relation between the graphs of the functions y = f(x) and y = f(–x) when

We have

Since both the functions are same, so the graphs of y = f(x) and y = f(–x) are identical.

Option (C) is CORRECT.

(2) We are to write equation of the function g(x) that translates the parent function  f(x) = x² by shifting g(x) 7 units to the left and 5 units down.

We know that

if a function y = f(x) is shifted a units to the left and 5 units down, then the new function is given by

For the given translation, a = 7  and  b = 5.

Therefore, the new function is given by

Thus, option (B) is CORRECT.