What transformation has changed the parent function f(x) = log3x to its new appearance shown in the graph below? a) f(x − 2) b) f(x + 2) c) f(x) − 2 d) f(x) + 2

Answer : option B

Parent Graph f(x) = is attached below

We analyze each option

A) f(x − 2) --> x - 2 shifts the graph 2 units to the right

B) f(x + 2) --> x + 2 shifts the graph 2 units to the left

C) f(x) − 2 --> f(x) - 2 shifts the graph 2 units down

D) f(x) + 2 --> f(x) + 2 shifts the graph 2 units up

In the graph of f(x)= , the x intercept at x=1

From the graph attached in the question, the x intercept at x=-1

Its means the parent graph is shifted 2 units to the left.

Option B: f(x + 2) --> x + 2 shifts the graph 2 units to the left

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)