Graphs, Functions, Models
Polynomial Functions
Exponential And Logarithmic Functions
Systems of Equations
Miscellany
100

Use the given conditions to write an equation for the line in slope-intercept form.


Slope = -6 passing through (4, -1)

What is y = -6x + 23?
100

Determine if each function is a polynomial function. For those that are, identify the degree.


a)f(x) = 5x3 - 3x7 + 6
b)g(x) = 3x4-2x-3+6x - 4
c)h(x) = -4x5+3x2 - 4⁄x
a)polynomial of degree 7
b)not a polynomial
c)not a polynomial
100
Convert to an exponential equation: log (x+4) = -0.5
What is 10^-0.5 = x + 4 ?
100

Evaluate the determinant.


146
-24-10
The determinant is 4.
100

Find the distance between the pair of points. If necessary, round your answer to two decimal places.


(3, -6) and (1, 4)
The distance is 10.20.
200
Let g(x) = (7x + 2) / (3x + 2) Find the domain of g(x).
What is: all real numbers except for x = -2/3
200

Divide using synthetic division.


(5x4 - 8x3 - 2x + 7) ÷ (x - 2)

The quotient is 5x3 + 2x2 + 4x + 6,
and the remainder is 19.
200

Solve the exponential equation by expressing each side as a power of the same base and then equating exponents.


94x-3 = 27
What is x=9⁄8?
200

Solve the system by the substitution method.


y=9 - x2
y=2x+1

(-4, -7) and (2, 5)
200

Find the vertex for the parabola.


f(x) = 2x2 - 6x + 5

The vertex is located at (3⁄2, 1⁄2).
300

Solve the absolute value equation.


|4x + 3 | = 9

What is {-3, 1.5}?

300

Use the Leading Coefficient Test and intercepts to graph the polynomial function.


f(x) = (x + 5)2(x + 1)2(x - 3)
Since the degree is odd and the leading coefficient is positive, the graph will fall on the left and rise on the right. From the multiplicity of the zeros, we see that the graph will touch the x-axis at -5 and -1 and will cross the x-axis at 3.
300

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.


ln(10 - x) = 3
What is 10 - e^3?
300

Let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers.


A first number decreased by three times a second number is 14. Twice the first number increased by the second number is 7. Find the numbers.

x - 3y = 14
2x + y = 7

x = 5 and y = -3
300

Use the formula A=P(1+r⁄n)nt or A = Pert.


Find the accumulated value of an investment of $7500 for 10 years at an interest rate of 6.5% if the money is compounded quarterly. Round your answer to the nearest cent.
The accumulated value is $14,291.69.
400

Given that f(x) = 3x^2 - 2x + 4, find f(a + 2)

What is: 3(a+2)^2 - 2(a+2) + 4 = 3a^2 +34a +12
400

The water temperature in the Pacific Ocean varies inversely as the water's depth. At a depth of 1000 meters, the water temperature is 4.4o Celsius. What is the water temperature at a depth of 2750 meters?

The temperature is 1.6o Celsius.
400
Express in terms of sums and differences of logarithms: log3x^3y^2
What is log 3 + 3logx + 2logy?
400

Solve the equation for x.


4x-3
-23
=-30
x = -2
400

Graph the inequality.


y ≥ x2 + 3

Graph is a parabola shifted up three units and shaded on the inside.
500

Evaluate the piecewise function at the given values of the independent variable.


f(x) = { 2x + 1, if x > 4
x2 - 3, if x ≤ 4
a)f(-1)
b)f(6)
c)f(4)
What is:
a)f(-1)=-2
b)f(6)=13
c)f(4)=13
500

One's intelligence quotient, or IQ, varies directly as a person's mental age and inversely as that person's chronological age. A person with a mental age of 25 and a chronological age of 20 has an IQ of 125. What is the mental age of a person with a chronological age of 40 and an IQ of 110?

The mental age is 44.
500

Solve the problem involving exponential growth or decay. Use the exponential growth/decay model
A = A0ek t to solve. Round your answer to one decimal place.

The half-life of aspirin in your bloodstream is 12 hours. How long will it take for the aspirin to decay to 70% of the original dosage?


It will take 6.2 hours.
500
Solve the system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
x + 2y - z = 1
y + 4z = -3
-x + y - 2z = 5
(-2, 1, -1)
500

For the function f(x)=x2 - 2x - 3,



a) find the vertex
b) find the x-intercepts
c) find the y-intercept
d) graph the parabola


a) The vertex is at (1, -4)
b) The x-intercepts are -1 and 3
c) The y-intercept is -3
d) The parabola has its vertex at (1, -4), it opens upward, and passes through the points
(0, -3), (-1, 0), and (3, 0).
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