Question

HELP PLEASE !!29. How do the graphs of the functions y = f(x) and y = f(–x) relate when

Answer 1

Answer:

29. The graphs reflect each other.

30. g(x)=(x+7)^2 -5

Step-by-step explanation:

Answer 2

Answer:  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

$f(x)=x^2.$

We have

$y=f(x)=x^2,\\\\y=f(-x)=(-x)^2=x^2.$

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

$g(x)=(x+a)^2-b.$

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

Therefore, the new function is given by

$g(x)=(x+7)^2-5.$

Thus, option (B) is CORRECT.