Math 101 Review 1

Midterm 1

Room Sections
Cat 061 022 025 029      
Matheson 109 014 015 028 030    
Nesbitt 111 010 012 013 027 031 033

Exam Coverage: 1.1-1.6
Date: Friday, February 1st 8-8:50 am


Recap of section 1.1:

Slope and equations of Lines:

Slope

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
point-slope form)
3. Equation of Horizontal line through the point (a, b): y = b
4. Equation of Vertical line through the point (a, b): x = a

Section 1.2

Properties of Exponents

(m/n: n is always the root; you can then raise to the math power under or outside the )

1.3 Functions:
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.

Quadratic Functions:
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

vertex.

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:
• Factoring
To solve a quadratic equation, you must
1. Have the equation set = 0
2. Factor
3. Set each factor = 0 and solve for the variable

The solutions to ax2 + bx +c =0



•Using the Quadratic Formula

Applications:
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

Solving Polynomials:
Recall, solving means to find the value for the variable that makes the equation true.

Have the equation set = 0
Factor
Set each factor = 0 and solve for the variable

Rational Functions:
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