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MATH 1324
REVIEW 1
Summer 1
5) 3x = y + 2
Determine whether the given ordered pair is a solution of
the given equation.
1) 5x + 2y - 21 = 0; (3, 3)
2) x2 + y2 - 6x + 4y = -11; (2, -3)
Graph the linear equation.
3) -x = 3y + 8
Find the x-intercepts and y-intercepts of the graph of the
equation.
6) -2x + 2y = -2
7) y = x2 + 8
Sketch the graph of the equation.
8) y = x2 + 4
4) -4x = y - 5
1
Find an equation of the the line satisfying the given
conditions.
19) Through (2, 9); parallel to 8x + 7y = 65
9) y = x3 + 8
Determine the vertex of the parabola.
20) f(x) = x2 - 6x + 15
21) y = -4(x - 1)2 + 3
Find the rule of a quadratic function whose graph has the
given vertex and passes through the given point.
22) vertex (8, 3); point (4, 19)
Find the slope of the line, if it is defined.
10) Through (-5, -7) and (-2, -2)
Solve the problem.
23) Suppose the supply and demand for a certain
videotape are given by:
1
1
supply: p = q2 ;demand: p = - q2
4
4
11) Through (-5, -4) and (-5, -8)
12) Through (7, 3) and (-5, 3)
+ 30
where p is price and q is quantity.
How many videotapes are supplied at a price of $
27?
Write an equation in slope-intercept form of a line
satisfying the given conditions.
2
13) m = - ; b = 5
3
24) Given the following revenue and cost
functions, find the break-even point to the
nearest tenth. (Recall that profit equals revenue
minus cost.)
R(x) = 60x - 2x2 ; C(x) = 24x + 98
Find the slope and the y-intercept of the line.
14) 2x - 3y = 16
Decide whether the pair of lines is parallel, perpendicular,
or neither.
15) 3x - 2y = 13
2x + 3y = -16
Give the equation of the vertical asymptote(s) of the
rational function.
6
25) g(x) =
8x + 5
16) 12x + 4y = 16
24x + 8y = 33
Give the equation of the horizontal asymptote of the
rational function.
6x + 4
26) g(x) =
x-1
Find an equation of the line with slope m that passes
through the given point. Put the answer in slope-intercept
form.
17) (-8, -5), m = 0
Classify the function as a linear, quadratic, or exponential.
27) f(x) = -8x2 + 5x - 3
Write an equation in standard form for a line passing
through the pair of points.
18) (4, -2) and (8, -9)
28) f(x) = 3 x-2
29) f(x) = 5x + 8
2
Graph the function.
30) f(x) = 4 x
Find the value of the expression.
1
31) log7
49
32) ln e
A) 0
B) e
C) 1
D) -1
Write the expression as the logarithm of a single number
or expression with a coefficient of 1. Assume all variables
represent positive numbers.
33) log 6 + log 54 - log 9
34) 3 ln (x + 3) - 6 ln (x2 + 7)
Write the expression as a sum and/or a difference of
logarithms with all variables to the first degree.
35) ln 5t9 v2
36) log
9x
17y
Evaluate the expression.
37) log7 0.270
Solve the problem.
38) The population growth of an animal species is
described by F(t) = 500 + 60 log3 (2t + 1) where
t is measured in months. Find the population
of this species in an area 40 month(s) after the
species is introduced.
3
Answer Key
Testname: REVIEW 1R SUMMER 12017
1) Yes
2) Yes
3)
8)
9)
4)
10) 1
5)
2
3
11) Undefined
12) 0
2
13) y = - x + 5
3
14) m =
16
2
;b=3
3
15)
16)
17)
18)
19)
20)
21)
Perpendicular
Parallel
y = -5
-7x - 4y = -20
8x + 7y = 79
(3, 6)
(1, 3)
22) f(x) = (x - 8)2 + 3
23) About 10
24) 14.7 or 3.3
5
25) x = 8
6) x-intercept: 1; y-intercept: -1
7) y-intercept (0, 8), no x-intercepts
26) y = 6
27) Quadratic
4
Answer Key
Testname: REVIEW 1R SUMMER 12017
28) Exponential
29) Linear
30)
31) -2
32) C
33) log 36
34) ln
35)
(x + 3)3
6
(x2 + 7)
1
ln 5 + 3 ln t + ln v
2
36) log 9 + log x - log 17 - log y
37) -0.6729
38) 740
5