Questions: -> The graph of a function f is illustrated to the right. Use the graph of f as the first step toward graphing each of the following functions. (a) F(x) = f(x) + 4 (b) G(x) = f(x + 4) (c) P(x) = -f(x) (d) H(x) = f(x + 2) - 1 (e) Q(x) = 1/2 f(x) (f) g(x) = f(-x) (g) h(x) = f(2x) (e) Choose the correct graph of Q(x) = 1/2 f(x) below. A. B. C. D. (f) Choose the correct graph of g(x) = f(-x) below.

-> The graph of a function f is illustrated to the right. Use the graph of f as the first step toward graphing each of the following functions. (a) F(x) = f(x) + 4 (b) G(x) = f(x + 4) (c) P(x) = -f(x) (d) H(x) = f(x + 2) - 1 (e) Q(x) = 1/2 f(x) (f) g(x) = f(-x) (g) h(x) = f(2x) (e) Choose the correct graph of Q(x) = 1/2 f(x) below. A. B. C. D. (f) Choose the correct graph of g(x) = f(-x) below.
Transcript text: $\mid \rightarrow \quad$ The graph of a function $f$ is illustrated to the right. Use the graph of $f$ as the first step toward graphing each of the following functions. (a) $F(x)=f(x)+4$ (b) $G(x)=f(x+4)$ (c) $P(x)=-f(x)$ (d) $H(x)=f(x+2)-1$ (e) $Q(x)=\frac{1}{2} f(x)$ (f) $g(x)=f(-x)$ (g) $h(x)=f(2 x)$ (e) Choose the correct graph of $Q(x)=\frac{1}{2} f(x)$ below. A. B. c. D. (f) Choose the correct graph of $g(x)=f(-x)$ below.
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the given function and its graph

The problem provides a graph of a function \( f(x) \) and asks to use this graph to determine the graph of other functions derived from \( f(x) \).

Step 2: Analyze the first function \( G(x) = f(x) + 4 \)

The function \( G(x) = f(x) + 4 \) represents a vertical shift of the graph of \( f(x) \) upwards by 4 units.

Step 3: Choose the correct graph for \( G(x) = f(x) + 4 \)

To find the correct graph, look for the graph that is identical to \( f(x) \) but shifted 4 units upwards.

Final Answer

The correct graph for \( G(x) = f(x) + 4 \) is option B.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Naturalism is a form of... Soft romanticism Extreme realism Grotesque Gothicism Transcendentalist Reactionism
failedAnswered
If f(x) = 2 sin x / (3 + cos x), then f'(x) = f'(5) =
failedAnswered
For 1993 -1994, the average cost of tuition and fees at public four-year universities was 2331 for full-time in-state students. Twenty years later, it had increased 240%. To the nearest dollar, what was the approximate cost for 2013-2014? The approximate cost was . (Round down to the nearest dollar.)
failedAnswered
Regression Equation Homework Grade (%) Test Grade (%) 59 50 69 64 80 75 75 64 51 46 88 69 78 70 Correlation coefficient r:
failedAnswered
The Bell family and the Lewis family each used their sprinklers last summer. The water output rate for the Bell family's sprinkler was 20 L per hour. The water output rate for the Lewis family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 35 hours, resulting in a total water output of 800 L. How long was each sprinkler used? Bell family's sprinkler: hours Lewis family's sprinkler: hours