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Chapter 1: Problem 78

Sketch a graph of the function and determine whether it is even, odd, or neither. Verify your answer algebraically. $$f(x)=5-3 x$$

Short Answer

Expert verified
The function \(f(x) = 5 - 3x\) is neither even nor odd.

Step by step solution

01

Sketching the Function

First step is to sketch the graph of the function \(f(x) = 5 - 3x\). This is a linear equation where -3 is the slope and 5 is the y-intercept. The graph starts at y-intercept at (0,5) and goes down as x increased due to negative slope.
02

Determine the Nature of Function

Next, we determine if the function is even, odd or neither. We will plug in \(-x\) for \(x\) in the function and simplify: \(f(-x) = 5 - 3(-x)= 5 + 3x\). Compare \(f(-x)\) and \(f(x)\), it's clear that \(f(-x) \neq f(x)\) and \(f(-x) \neq -f(x)\).
03

Conclusion of Analysis

Based on the results of the test in Step 2, the function \(f(x) = 5 - 3x\) is neither even nor odd.

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