Chapter 1 | Functions and Graphs
17
Finding Zeros and y -Intercepts of a Function
Consider the function f ( x ) =−4 x +2. a. Find all zeros of f . b. Find the y -intercept (if any). c. Sketch a graph of f .
Solution a. To find the zeros, solve f ( x ) =−4 x +2=0. We discover that f has one zero at x =1/2. b. The y -intercept is given by ⎛ ⎝ 0, f (0) ⎞ ⎠ = (0, 2). c. Given that f is a linear function of the form f ( x ) = mx + b that passes through the points (1/2, 0) and (0, 2), we can sketch the graph of f ( Figure 1.9 ).
Figure 1.9 The function f ( x ) =−4 x +2 is a line with x -intercept (1/2, 0) and y -intercept (0, 2).
Example 1.4 Using Zeros and y -Intercepts to Sketch a Graph
Consider the function f ( x ) = x +3+1. a. Find all zeros of f . b. Find the y -intercept (if any). c. Sketch a graph of f .
Solution a. To find the zeros, solve x +3+1=0. This equation implies x +3=−1. Since x +3≥0 for all
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