Exam Coverage: 1.1-1.6
Date: Friday, February 1st 8-8:50 am
Recap of section 1.1:
Slope and equations of Lines:
Formula for slope:
1. Slope of a horizontal line is 0
2. Slope of a vertical line is undefined
Equations of Lines:
1. Use slope-intercept form (y = mx + b) if you are given
-The slope and the y-intercept
2.Use point-slope form if you are given
- The slope (m) and any point on the line,
- You are given two points on the line only (find the slope first, then pick a point and use
3. Equation of Horizontal line through the point (a, b): y = b
4. Equation of Vertical line through the point (a, b): x = a
Properties of Exponents
(m/n: n is always the root; you can then raise to the math power under or outside the )
Domain and Range:
x = input value = independent variable; domain describes allowable values for x;
f(x) = y = output value = dependent variable; range describes possible output for f(x)
The Vertical Line Test:
A curve in the Cartesian plane is the graph of a function if and only if, if no vertical line intersects the
curve at more than one point.
Types of Functions:
Linear Function: A linear function is a function that can be expressed in the form f(x) = mx +b with
constants m and b. Its graph is a line with slope m and y-intercept b.
A quadratic function is a function that an be expressed
in the form
f(x) = ax2 + bx +c
with coefficients , a≠0, b and c.
Its graphs is called a parabola
In the equation f(x) = ax2 + bx +c.
If a>0, the parabola opens up and has a minimum.
If a<0, the parabola opens up and has a maximum.
The minimum or maximum value of a parabola is called its
To find the vertex of quadratic functions:
Again, the vertex is the highest or lowest point of a parabola. To find the vertex of a parabola:
Solving Quadratic Equations:
A value of x that solves an equation f(x) = 0 is called a root of the equation or the x-intercept of the
graph of y = f(x)
There are 2 methods to solve a quadratic equation:
To solve a quadratic equation, you must
1. Have the equation set = 0
3. Set each factor = 0 and solve for the variable
The solutions to ax2 + bx +c =0
•Using the Quadratic Formula
Profit, Revenue, and Cost:
Revenue: Revenue is the amount of money a company takes in from producing x items.
Cost: The cost is how much it costs for the company to make the same x items.
Profit = Revenue – Cost A company breaks even if Revevue = Cost
Section 1.4 Functions Continued…
A Polynomial Function is a function that can be written in the form:
The domain is all Real numbers.
The degree is the highest power of the variable
Recall, solving means to find the value for the variable that makes the equation true.
Have the equation set = 0
Set each factor = 0 and solve for the variable
A rational function is a fraction consisting of one polynomial divided by another polynomial.
Domain: division by zero is undefined, so the domain of a rational function is all real numbers, except
those which make the denominator 0.
Piecewise Linear Functions:
A piecewise linear function is a function which is given in several parts. For example
The Difference Quotient