# Information is given about a polynomial f(x) whose coefficients are real numbers

. Evaluate the expression using the values given in the table. 1)

(gHf)(1)

x 1 4 9 12

f(x) -4 9 0 15

x -5 -4 1 3

g(x) 1 -6 4 9

1) Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. 2) Degree 4; zeros: 6 – 5i, 7i 2) Decide whether or not the functions are inverses of each other. 3)

f(x) =

8 + x

x

, g(x) =

8

x – 1 3) Use the given zero to find the remaining zeros of the function. 4) f(x) = x3 + 2×2 – 6x + 8; zero: 1 + i 4) Give the equation of the horizontal asymptote, if any, of the function. 5)

f(x) =

x

2 – 7

49x – x4

5) 1

Find the domain of the composite function f H g. 6)

f(x) =

7

x + 8

; g(x) = x + 4

6) Solve the equation. 7) 2

1 + 2x = 32 7) 8) 16x – 4 = 8

4x 8) 9) log2(3x – 2) – log2(x – 5) = 4 9) Change the exponential expression to an equivalent expression involving a logarithm. 10)

5

-2 =

1

25 10) Solve the problem. 11)

The size P of a small herbivore population at time t (in years) obeys the function

P(t) = 900e

0.13t

if they have enough food and the predator population stays constant. After

how many years will the population reach 2700? Round to the nearest hundredth. 11) 2

12)

Sandy manages a ceramics shop and uses a 700°F kiln to fire ceramic greenware. After

turning off her kiln, she must wait until its temperature gauge reaches 175°F before

opening it and removing the ceramic pieces. If room temperature is 70°F and the gauge

reads 600°F in 5 minutes, how long must she wait before opening the kiln? Assume the kiln

cools according to Newton’s Law of Cooling:

U = T + (Uo – T)e

kt

.

(Round your answer to the nearest whole minute.) 12) Give the equation of the horizontal asymptote, if any, of the function. 13)

f(x) =

-x2 + 16

x2 + 5x + 4 13) Use the graph to find the oblique asymptote, if any, of the function. 14) 14) 3

Answer Key

Testname: MTH 167 TEST 2 STUDY GUIDE SUMMER 2022

1) -6

2) 6 + 5i, -7i

3) Yes 4) 1 – i, -4

5) y = 0 6) {x x J -12}

7) {2}

8) – 2 9) {6} 10)

log 5

1

25 = -2

11) 8.45 yr 12) 52 minutes 13) y = -1

14) y = x 4