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Practice Test A

Find the equation of a circle (in standard form) having a diameter with endpoints $(- 2, 3)$ $(- 2, 3)$ and $(- 4, 5) .$ $(- 4, 5) .$
Determine which symmetries the graph of the equation $3 x + 2 x y^{2} = 1$ $3 x + 2 x y^{2} = 1$ has.
Find the x- and y-intercepts of the graph of $y = x^{2} (x - 3) (x + 1) .$ $y = x^{2} (x - 3) (x + 1) .$
Graph the equation $x^{2} + y^{2} - 2 x - 2 y = 2 .$ $x^{2} + y^{2} - 2 x - 2 y = 2 .$
Write the slope–intercept form of the equation of the line with slope $- 1$ $- 1$ passing through the point (2, 7).
Write an equation of the line parallel to the line $8 x - 2 y = 7$ $8 x - 2 y = 7$ passing through $(2, - 1) .$ $(2, - 1) .$
Use $f (x) = - 2 x + 1$ $f (x) = - 2 x + 1$ and $g (x) = x^{2} + 3 x + 2$ $g (x) = x^{2} + 3 x + 2$ to find (fg)(2).
Use $f (x) = 2 x - 3$ $f (x) = 2 x - 3$ and $g (x) = 1 - 2 x^{2}$ $g (x) = 1 - 2 x^{2}$ to evaluate g(f(2)).
Use $f (x) = x^{2} - 2 x$ $f (x) = x^{2} - 2 x$ to find $(f \circ f) (x) .$ $(f \circ f) (x) .$
If $f (x) = {\begin{array}{l} x^{3} - 2 & if & x \leq 0 \\ 1 - 2 x^{2} & if & > 0 \end{array}$ $f (x) = {\begin{array}{l} x^{3} - 2 & if & x \leq 0 \\ 1 - 2 x^{2} & if & > 0 \end{array}$ , find (a) $f (- 1),$ $f (- 1),$ (b) f(0), and (c) f(1).
Find the domain of the function $f (x) = \frac{\sqrt{x}}{\sqrt{1 - x}} .$ $f (x) = \frac{\sqrt{x}}{\sqrt{1 - x}} .$
Determine the average rate of change of the function $f (x) = 2 x + 7$ $f (x) = 2 x + 7$ between $x = 1$ $x = 1$ and $x = 4 .$ $x = 4 .$
Determine whether the function $f (x) = 2 x^{4} - \frac{3}{x^{2}}$ $f (x) = 2 x^{4} - \frac{3}{x^{2}}$ is even, odd, or neither.
Find the intervals where the function whose graph is shown in the second column is increasing or decreasing.
Starting with the graph of $y = \sqrt{x},$ $y = \sqrt{x},$ describe the sequence of transformations (in order) required to sketch the graph of $f (x) = 2 \sqrt{x - 3} + 4 .$ $f (x) = 2 \sqrt{x - 3} + 4 .$
A ball is thrown upward from the ground. After t seconds, the height h (in feet) above the ground is given by $h = 25 - {(2 t - 5)}^{2} .$ $h = 25 - {(2 t - 5)}^{2} .$ How many seconds does the ball take to reach a height of 25 feet?
Assuming that f is a one-to-one function and $f (2) = 7,$ $f (2) = 7,$ find $f^{- 1} (7) .$ $f^{- 1} (7) .$
Find the inverse function $f^{- 1} (x)$ $f^{- 1} (x)$ of the one-to-one function

$f (x) = \frac{2 x}{x - 1} .$ $f (x) = \frac{2 x}{x - 1} .$
Now that Jo has saved $1000 for a car, her dad takes over and deposits $100 in her account each month. Write an equation that relates the total amount of money, A, in Jo’s account to the number of months, x, that Jo’s dad has been putting money in her account.
The cost C in dollars for renting a car for one day is a function of the number of miles traveled, m. For a car renting for $30.00 per day and $0.25 per mile, this function is given by

$C (m) = 0.25 m + 30 .$ $C (m) = 0.25 m + 30 .$
1. Find the cost of renting the car for one day and driving 230 miles.
2. If the charge for renting the car for one day is $57.50, how many miles were driven?

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Table of Contents for Practice Test A

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Table of Contents for
Practice Test A