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	Precalculus Functions and Graphs 4/e Barnett/Ziegler/Byleen
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Chapter 2: Graphs and Functions

Worked Exercises

Chapter 2: Graphs and Functions

Exercise Set 2-1

The figure shows a portion of a graph. Extend the given graph to one that exhibits the indicated type of symmetry.

Solution

Determine whether the given points are vertices of a right triangle. (Recall, a triangle is a right triangle if and only if the square of the longest side is equal to the sum of the squares of the shorter sides.)

Solution

Find the perimeter (to two decimal places) of the triangle with the indicated vertices.

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Find the center and radius of the circle with the given equation. Graph the equation.

Solution

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Find the equation of a circle that has a diameter with the given end-points.

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APPLICATION

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Exercise Set 2-2

Write an equation of the line that contains the indicated point(s) and/or has the indicated slope and/or has the indicated intercepts. Write the final equation in the slope-intercept from y = mx in the form x = c.

Solution

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Write an equation of the line that contains the indicated point and meets the indicated condition(s). Write the final answer in standard form Ax + By = C, A >= 0.

Solution

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The problem is calculus-related. Recall that a line tangent to a circle at a point is perpendicular to the radius drawn to that point (see the figure). Find the equation of the line tangent to the circle at the indicated point. Write the final answer in the standard form Ax + By = C, A >= 0. Graph the circle and the tangent line on the same coordinate system.

Solution

Exercise Set 2-3

Indicate whether each set defines a function. Find the domain and range of each function.

Solution

The problem refers to the functions

Evaluate as indicated.

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Determine if the equation defines a function with independent variable x. If it does, find the domain. If it does not, find a value of x to which there corresponds more than one value of y.

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Find the domain of the indicated function.

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Find and simplify:

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APPLICATION

Solution

Exercise Set 2-4

The problem refers to function f given by the following graph. (Assume that the graph continues as indicated beyond the parts shown.)

Solution

The problem describes the graph of a continuous function f over the interval [-5, 5]. Sketch the graph of the function that is consistent with the given information.

Solution

Find the linear function f satisfying the given conditions.

Solution

Graph the expression, finding the axis, vertex, maximum or minimum, and range.

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Graph the expression, finding the axis, vertex, x intercepts, and y intercept.

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Graph the expression, finding the axis, vertex, intervals over which f is increasing, and intervals over which f is decreasing.

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Graph the expression, finding the domain, range, and any points of discontinuity.

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Graph the expression, finding the axis, vertex, maximum or minimum of f(x), range, intercepts, intervals over which f is increasing, and intervals over which f is decreasing.

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Write a piecewise definition for f and sketch the graph of f. Include sufficient intervals to clearly illustrate both the definition and the graph. Find the domain, range, and any points of discontinuity.

Solution

Exercise Set 2-5

For the indicated functions f and g, find the functions f + g, f -g, fg, and f/g, and find their domains.

Solution

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For the indicated functions f and g, find the functions f ° g, and g ° f and find their domains.

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The graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using -5 <= x <= 5 and -5 <= y <= 5.

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Exercise Set 2-6

Determine if the following function is one-to-one.

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The following function is one-to-one. Find f^-1.

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The graph of the function is one-quarter of the graph of the circle with radius 1 and center (0, 1). Find f^-1, find the domain and range of f^-1, and sketch the graphs of f and f^-1 in the same coordinate system.

Solution

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