Given the graphs of the functions f and g complete the following: a) Find (f − g)(2). b) Find (fg)(3). c) Find (g/f)(1) d) Find (f ∘g)(−2)
Transcribed Image Text:### Problem 4: Function Analysis Based on Graphs
Given the graphs of the functions \( f \) and \( g \), complete the following:
#### Graph Explanation:
The given figure shows the graphs of two functions, \( f \) and \( g \), overlaid on a coordinate grid. The \(x\)- and \(y\)-axes are labeled, with the \(x\)-axis marked at integer intervals. The functions are distinguished by color:
- The function \( f \) is represented by a red piecewise linear graph.
- The function \( g \) is represented by a blue sinusoidal curve.
### Tasks:
a) **Find \( (f - g)(2) \):**
Determine the values of \( f(2) \) and \( g(2) \) from their respective graphs, and then find their difference:
\[
(f - g)(2) = f(2) - g(2)
\]
b) **Find \( (fg)(3) \):**
Determine the values of \( f(3) \) and \( g(3) \) from their respective graphs, and then find their product:
\[
(fg)(3) = f(3) \cdot g(3)
\]
c) **Find \( \left(\frac{g}{f}\right)(1) \):**
Determine the values of \( g(1) \) and \( f(1) \) from their respective graphs, and then find their quotient:
\[
\left(\frac{g}{f}\right)(1) = \frac{g(1)}{f(1)}
\]
d) **Find \( (f \circ g)(-2) \):**
Determine the value of \( g(-2) \) from its graph, and then find \( f \) evaluated at this value:
\[
(f \circ g)(-2) = f(g(-2))
\]
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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![### Problem 4: Function Analysis Based on Graphs
Given the graphs of the functions \( f \) and \( g \), complete the following:
#### Graph Explanation:
The given figure shows the graphs of two functions, \( f \) and \( g \), overlaid on a coordinate grid. The \(x\)- and \(y\)-axes are labeled, with the \(x\)-axis marked at integer intervals. The functions are distinguished by color:
- The function \( f \) is represented by a red piecewise linear graph.
- The function \( g \) is represented by a blue sinusoidal curve.
### Tasks:
a) **Find \( (f - g)(2) \):**
Determine the values of \( f(2) \) and \( g(2) \) from their respective graphs, and then find their difference:
\[
(f - g)(2) = f(2) - g(2)
\]
b) **Find \( (fg)(3) \):**
Determine the values of \( f(3) \) and \( g(3) \) from their respective graphs, and then find their product:
\[
(fg)(3) = f(3) \cdot g(3)
\]
c) **Find \( \left(\frac{g}{f}\right)(1) \):**
Determine the values of \( g(1) \) and \( f(1) \) from their respective graphs, and then find their quotient:
\[
\left(\frac{g}{f}\right)(1) = \frac{g(1)}{f(1)}
\]
d) **Find \( (f \circ g)(-2) \):**
Determine the value of \( g(-2) \) from its graph, and then find \( f \) evaluated at this value:
\[
(f \circ g)(-2) = f(g(-2))
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