By Marcel Finan
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Extra resources for A semester course in trigonometry
1 (e) j(x) = √x+4 . 7 Graph each function. Insert solid circle or hollow circles to indicate the true nature of the function. (a) f (x) = |x|, if x ≤ 1 2, if x > 1. (b) g(x) = 4, if x ≤ −1 x2 , if −1 < x < 1 −x + 5, if x ≥ 1. 8 Use the vertical line test to determine which of the following graphs are graphs of functions. 9 Use the indicated graphs to indentify the intervals over which the function 37 is increasing, constant, or decreasing. 10 Use the horizontal line test to determine which of the following functions are one-to-one.
Reflections and Symmetry Reflections occur when either the input or the output of a function is multiplied by -1. Reflection About the x-Axis For a given function f (x), the points (x, f (x)) and (x, −f (x)) are on opposite sides of the x-axis. So the graph of the new function −f (x) is the reflection of the graph of f (x) about the x-axis. 1 Graph the functions f (x) = 2x and −f (x) = −2x on the same axes. Solution. 1. 1 Reflection About the y-Axis We know that the points (x, f (x)) and (−x, f (x)) are on opposite sides of the y-axis.
A) Sketch a graph of the cost function C as a function of the distance traveled x, assuming that 0 ≤ x ≤ 1. (b) Find a formula for C in terms of x on the interval [0, 1]. (c) What is the cost for a 54 − mile ride? Solution. 7. 50 (c) The cost for a 4 5 if x = 0 if 0 < x ≤ 51 , if 51 < x ≤ 25 , if 25 < x ≤ 35 , if 35 < x ≤ 45 , if 45 < x ≤ 1. 25. 33 Increasing and Decreasing Functions We say that a function is increasing if its graph climbs as x moves from left to right. That is, the function values increase as x increases.