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MC 2025 In-Course Diagnostic Quizzes P1

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The manager of a weekend flea market knows from past experience that if he charges x dollars for a rental space at the market, then the number y of spaces he can rent is given by the equation . What does the x-intercept indicate?
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The graphs of f(x) and g(x) are given. For what values of x is f(x) = g(x)?

Two parabolas are graphed on the x y coordinate plane. One parabola, labeled f, enters the bottom left of the viewing window in the third quadrant, goes up and to the right, passes through the approximate point (–10, –11.8) to reach the vertex at (4, 10), goes down and to the right, passes through the approximate point (18, –11.8), and then exits the bottom right of the viewing window. Another parabola, labeled g, enters the top left of the viewing window in the second quadrant, goes down and to the right, passes through the point (–8, 18.0) to reach the vertex at (4, 2), goes up and to the right, passes through the point (16, 18.0), and then exits the top right of the viewing window. Both the parabolas intersect at the points (–2, 6) and (10, 6).

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The graph of the function f follows. Choose the graph of .

A line is plotted on x y coordinate plane. The line enters the bottom left of the viewing window, goes up and to the right crosses the y-axis at (0,-3) and x-axis at (3,0), then exits the top right of the viewing.

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The graph of the function   follows. Choose the graph of y = - 1 over 2 f(-x).

A curve is graphed on the x y coordinate plane. The curve consists of the points (negative 2, 0), (negative 1, negative 1), (0, 1), and (2, negative 2) connected by line segments.

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Suppose that the graph of  f  is given. Describe how the graph of the function y = f(x - 5) - 5 can be obtained from the graph of  f.

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Sandy wishes to have a rectangular garden in her backyard. She has 80 ft of fencing with which to enclose her garden. Letting x denote the width of the garden, find a function f in the variable x that gives the area of the garden.

                             A figure consists of a rectangle of length y units and width x units.

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If the point  is on the graph of an even function, what other point must also be on the graph?

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If and , find a function g such that .

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Identify the type of the following function.

 

 

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Find the function  and its domain if  and

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