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.
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.
Solution
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.