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Graphs, Functions, and Models
Polynomial Functions
Exponential and Logarithm Functions
Systems of Equations
Quadratic Functions
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+5) = 2
What is "10^2 = x + 5"?
100
Does (-1, 3) satisfy the following system of equations? x + y = -2 y = x - 8
What is "no"?
100
Solve. Find exact solutions. x^4 - 2x^2 - 8 = 0
What is "{-2, 2,}"?
200
Find the domain of the function: g(x) = (2x + 5)/(3x - 2)
What is "all real numbers except 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
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

What is "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 external behavior and x-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(2 - x) = 3
x = -6
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
A farmer wants to enclose a rectangular pen for sheep using 120 feet of fencing. The side of the barn will be used as one side of the rectangle. Find the dimensions for which the area is a maximum.
What is "30 feet by 60 feet" with the 60 foot side parallel to the barn?
400

Given that f(x) = 3x^2 - 2x + 7, find and simplify f(a+3).

What is "3(a+3)^2 - 2(a+3) + 7 = 3a^2 +16a +28"?
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: log(3x^4)/y^2
What is "log 3 + 4log x - 2log y"?
400
Solve using the elimination method: x + 2y = 7 x - 2y = -5
What is (1, 3)?
400

Graph the equation.


y = x2 + 3

What is: "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
DAILY DOUBLE

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?


What is "6.2 hours"?
500
Set up the system of equations for the following problem: One evening, 1500 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $25 for a covered pavilion seat and $15 for a lawn seat. Total receipts were $28,500. How many of each type of ticket were sold. DO NOT SOLVE
What is: 25x + 15y = 28500 and x + y = 1500"?
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

What is:
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).