136k views
0 votes
HELP PLEASE !!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

2 Answers

0 votes

Answer:

29. The graphs reflect each other.

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

Explanation:

User Dpedro
by
8.0k points
3 votes

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.

User Eten
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories