**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 1 ^{st} 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) = ax^{2} + bx +c

with coefficients , a≠0, b and c.

Its graphs is called a **parabola**

In the equation f(x) = ax^{2} + 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 ax^{2} + 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