Questions: Question 19 of 25 The graph of the reciprocal parent function, f(x)=1/x, is shifted 7 units up and 2 units to the right to create the graph of g(x). What function is g(x) ? A. g(x)=1/(x+7)+2 B. g(x)=1/(x-2)+7 C. g(x)=1/(x-7)+2 D. g(x)=1/(x+2)+7

Question 19 of 25
The graph of the reciprocal parent function, f(x)=1/x, is shifted 7 units up and 2 units to the right to create the graph of g(x). What function is g(x) ?
A. g(x)=1/(x+7)+2
B. g(x)=1/(x-2)+7
C. g(x)=1/(x-7)+2
D. g(x)=1/(x+2)+7

Transcript text: Question 19 of 25 The graph of the reciprocal parent function, $f(x)=\frac{1}{x}$, is shifted 7 units up and 2 units to the right to create the graph of $g(x)$. What function is $g(x)$ ? A. $g(x)=\frac{1}{x+7}+2$ B. $g(x)=\frac{1}{x-2}+7$ C. $g(x)=\frac{1}{x-7}+2$ D. $g(x)=\frac{1}{x+2}+7$

Solution

Solution Steps

Step 1: Understand the transformations

The parent function is $ f(x) = \frac{1}{x} $. To shift the graph 7 units up, we add 7 to the function. To shift the graph 2 units to the right, we replace $ x $ with $ (x - 2) $.

Step 2: Apply the vertical shift

Shifting the graph 7 units up modifies the function to: \[ f(x) = \frac{1}{x} + 7 \]

Step 3: Apply the horizontal shift

Shifting the graph 2 units to the right modifies the function to: \[ g(x) = \frac{1}{x - 2} + 7 \]

Step 4: Match the function with the options

The function $ g(x) = \frac{1}{x - 2} + 7 $ corresponds to option B.