Add or subtract as indicated and write the result in standard form.
1) 3 – (- 3 + 3i) – (- 3 – 7i)
A) 9 + 4i B) 6 + 4i C) 9 – 4i D) 6 – 4i
Divide and express the result in standard form.
2) 8
9 + i
A) 9
10 +
1
10 i B) 36
41 +
4
41 i C) 36
41 – 4
41 i D) 9
10 – 1
10 i
Find the axis of symmetry of the parabola defined by the given quadratic function.
3) f(x) = (x + 2)2 + 4
A) x = 2 B) y = – 4 C) x = -2 D) y = 4
Find the horizontal asymptote, if any, of the graph of the rational function.
4) g(x) = 10×2
2×2 + 1
A) y = 1
5 B) y = 0
C) y = 5 D) no horizontal asymptote
5) f(x) = 9x
3×2 + 1
A) y = 1
3 B) y = 0
C) y = 3 D) no horizontal asymptote
Find the vertical asymptotes, if any, of the graph of the rational function.
6) g(x) = x
x(x – 3)
A) x = 3 B) x = 0 and x = -3
C) x = 0 and x = 3 D) no vertical asymptote
7) h(x) = x + 6
x2 – 36
A) x = -6 B) x = 6
C) x = 6, x = -6 D) no vertical asymptote
Perform the indicated operations and write the result in standard form.
8) -36 + -64
A) 14i B) -14 C) -14i D) 48i
9) ( – 36)( – 9)
A) -18i B) 18 C) -18 D) 18i2
2
Solve the quadratic equation using the quadratic formula. Express the solution in standard form.
10) 6×2 – 5x + 3 = 0
A) 5
12 ±
47
12 B) – 5
12 ±
47
12 C) – 5
12 ± i 47
12 D) 5
12 ± i 47
12
SHORT ANSWER. You must show all your work to receive full credit.
For the polynomial, state (a.) the degree (b.) whether it is odd or even or neither (c.) end behavior (d.) number of zeros
and multiplicities if any. (e.) Graph the polynomial function.
11) f(x) = x4 – 9×2
Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given
integers.
12) f(x) = 2×5 – 9×3 – 7×2 + 6; between 2 and 3
Solve the polynomial inequality. Express the solution set in interval notation.
13) x2 – 4x – 12 K 0
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval
notation.
14) x – 1
x + 7
> 0
Solve the problem.
15) An arrow is fired straight up from the ground with an initial velocity of 192 feet per second. Its height, s(t), in
feet at any time t is given by the function s(t) = – 16t2 + 192t. Find the interval of time for which the height of the
arrow is greater than 252 feet.
3
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