Pre-Calculus

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1.

Which of these is the equation of a parabola with vertex (–6, 2)?

A.

*y *= 4(*x *+ 6)2 + 2

B.

*y *= (*x *+ 6)2 + (–2)

C.

*y *= 4*x*2 + 6*x *− 2

D.

*y *= *x*2 + 12*x *+ 34

2.

The square root property tells us that if (2*x *− 9)2 = 9 is true then which of the following *must *also be

true?

A.

2*x *− 9 = ±9

B.

2*x *− 9 = ±3

C.

2*x *= ±0

D.

2*x *= ±18

3.

The solution set for 4*x*2 − 3*x *− 1 ≥ 0 is which of these?

A.

B.

C.

D.

4.

The solution set for is which of these?

A.

B.

C.

D.

5.

What is the result of performing partial fraction decomposition on the rational function ?

A.

B.

C.

D.

6.

Which is a *correct *setup for the partial fraction decomposition of ?

A.

B.

C.

D.

7.

Which are the solutions to *x*2 = –16?

A.

4 and –4

B.

–4 and 4

C.

4*i *and –4*i*

D.

4 + *i *and 4 − *i*

8.

The solution set for *y *> 6*x *− *x*2 is shown in which of these graphs?

A.

B.

C.

D.

9.

Choose the one *true *statement about .

A.

It has a vertical asymptote at *x *= 1.

B.

It is an odd function.

C.

It has a horizontal asymptote at *y *= 0.

D.

It has no vertical asymptotes.

10.

The function *f*(*x*) = 6*x*3 − 6*x *has which symmetry or symmetries?

A.

It is neither an even function nor an odd function.

B.

It is an even function.

C.

It is an odd function.

D.

It is both an even and an odd function.

11.

Which graph below shows the inverse of the function *y *= *x*3?

A.

B.

C.

D.

12.

Which of these statements is *true *about the graph of the equation *y *= *x*2 − *x *− 1?

A.

It is a parabola with axis of symmetry .

B.

It is a parabola with axis of symmetry .

C.

It is a parabola with vertex at .

D.

It is a parabola with vertex at .

13.

The solutions to *x*2 + *x *− 5 = 0 are which of these?

A.

B.

C.

D.

14.

Compute when *f*(*x*) = –2*x*2 + 4.

A.

B.

C.

D.

15.

A.

B.

C.

D.

16.

Consider the functions *f*(*x*) = 2*x *+ 13 and *g*(*x*) = *x*2 − 1. What is *f/g *and what is its domain?

A.

with domain (–∞, –1) ∪ (–1, 1) ∪ (1, ∞)

B.

with domain {–1, 1}

C.

You cannot compute *f/g *because *g*(*x*) ≠ 0.

D.

with domain all real numbers

17.

What is the inverse of .

A.

*f*–1(*x*) = (*x*2 − 9)

B.

*f*–1(*x*) = (*x*2 + 9)

C.

*f*–1(*x*) = (*x *− 9)2

D.

*f*–1(*x*) = (*x *+ 9)2

18.

Which of the following functions satisfies *f*(2.1) = 6?

A.

B.

C.

D.

19.

Which of the following is the solution set for the inequality ?

A.

B.

C.

D.

20.

The function *f*(*x*) = –*x*2 + 17 has which symmetry or symmetries?

A.

It is an even function.

B.

It is neither an even function nor an odd function.

C.

It is an odd function.

D.

It is both an even and an odd function.

21.

Which of the following choices lists the approximate solutions to the quadratic equation .3*x*2 − 8.1*x *+

0.9 = 0?

A.

0.0111 and 26.888

B.

–14.8489 and –12.1511

C.

14.8489 and 12.1511

D.

–0.0111 and –26.888

22.

Does the piecewise function ever achieve the value 12?

A.

No, because its range includes no numbers higher than 10, at *x *= 0.

B.

Yes, once, at .

C.

Yes, once, at *x *= 12.

D.

Yes, twice, once on each side of the *y *axis.

23.

Choose the one *true *statement about .

A.

It has a slant asymptote at .

B.

It is an even function.

C.

It has vertical asymptotes at *x *= 2 and *x *= 1.

D.

It has a horizontal asymptote at .

24.

Which of these is the first step in solving *x*2 + 6*x *+ 1 = 0 by completing the square?

A.

*x*2 + 6*x *= –1

B.

(*x *+ 6)2 + 1 = 1

C.

(*x *+ 6)2 = –1

D.

*x*2 + 6*x *+ 9 − 9 + 1 = 0

25.

Solve *kPt*2 − *Rt *= 0 for *t*, assuming *t *> 0. Which of these describes your answer?

A.

is the only solution.

B.

is the only solution.

C.

*t *and *kP *− *R *are both solutions.

D.

and 0 are both solutions.

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