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

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