Question

question 42 (1 point)
write a rule for g that represents the indicated transformations of the graph of f.
$f(x) = 3x^5 - 3$; translation 1 unit left, followed by a reflection in the y - axis
a $g(x) = -3(x + 1)^5 + 3$
b $g(x) = -3(x - 1)^5 + 3$
c $g(x) = 3(-x + 1)^5 - 3$
d $g(x) = 3(-x - 1)^5 - 3$

Explanation:

Step1: Apply translation 1 unit left

To translate a function \( f(x) \) 1 unit left, we replace \( x \) with \( x + 1 \) in the function. So for \( f(x)=3x^{5}-3 \), after translating 1 unit left, we get \( f(x + 1)=3(x + 1)^{5}-3 \).

Step2: Apply reflection in the y - axis

To reflect a function \( y = h(x) \) in the \( y \) - axis, we replace \( x \) with \( -x \) in the function. Let \( h(x)=3(x + 1)^{5}-3 \), after reflecting in the \( y \) - axis, we have \( g(x)=h(-x)=3(-x + 1)^{5}-3 \).

Answer:

c. \( g(x)=3(-x + 1)^{5}-3 \)