# Ch 15: ELM Test - Geometry: Graphing Functions

### About This Chapter

## ELM Geometry: Graphing Functions - Chapter Summary

Get ready for the ELM math exam by watching these online videos. Then test what you've learned with our interactive online quizzes. Lessons in this chapter cover:

- Plotting Points to Graph Functings
- Linear Equations: Intercepts, Standard Form and Graphing
- Finding and Applying the Slope of a Line
- Finding and Applying the Slope-Intercepts of a Line
- Graphing Undefined Slope, Zero Slope and More
- Determining the Equation of a Line Using Point-Slope Formula
- Using The Distance Formula
- Using The Midpoint Formula
- Understanding Parabolas in Standard, Intercept and Vertex Forms
- Graphing Cubics, Quartics, Quintics and Beyond

Each lesson will explain these important mathematical concepts and use relatable examples to bring them to life. Watch the videos as often as you'd like or read over our complete transcripts to review what you've learned.

## ELM Objectives

The ELM is a math proficiency exam required for all incoming students to schools in the California State University system. You can learn more about the topics on the ELM.

The lessons in this chapter are part of the larger Geometry portion of the ELM. Geometry constitutes about 30% of the overall ELM. Other Geometry topics covered in this online course include:

- Defining and Understanding Properties of Objects
- Calculating Area, Perimeter and Volume
- Graphing Functions
- Using the Pythagorean Theorem

The lessons in this chapter and the others in the ELM course can prepare a student for success on the ELM placement exam.

### 1. Graph Functions by Plotting Points

Let's say you have a function. What does it look like? How do you graph it? In this lesson, we'll learn how to graph functions by determining and plotting points.

### 2. Identify Where a Function is Linear, Increasing or Decreasing, Positive or Negative

Functions do all kinds of fun things. In this lesson, learn how to identify traits of functions such as linear or nonlinear, increasing or decreasing and positive or negative.

### 3. Linear Equations: Intercepts, Standard Form and Graphing

Do you know what to do if an equation doesn't look like y=mx+b?! If not, then this video is for you. Chances are the equation is in standard form, so we'll learn how to use standard form equations, how to graph them and why they can be helpful.

### 4. How to Find and Apply The Slope of a Line

In this lesson, we'll discover all about the slopes of lines. We'll learn about different types of slopes and how to find the slopes of lines. We'll use two methods: the slope formula and the slope-intercept form.

### 5. How to Find and Apply the Intercepts of a Line

How can you take an equation of a line and find out where it will cross the x- or y-axis? In this lesson, we'll define x-intercepts and y-intercepts and learn how to find them.

### 6. Graphing Undefined Slope, Zero Slope and More

There are two special cases when it comes to slopes on the xy plane: horizontal and vertical lines. Without any more information, these examples can be pretty confusing. But with a little instruction, they end up being some of the easiest lines to graph!

### 7. Equation of a Line Using Point-Slope Formula

It's time for a road trip to Las Vegas, and after four hours of driving at 60 mph ... Are we there yet? Learn the point-slope form of the equation of a line to help answer this age-old question.

### 8. How to Use The Distance Formula

You can't always rely on your smartphone to tell you how far you need to travel to get from point A to point B. The distance formula will tell you the distance between any two points on a graph. In this lesson, you'll learn where it comes from and how to use it!

### 9. How to Use The Midpoint Formula

The formula for the midpoint of a line segment will tell you how to find the middle of any line segment on the x, y plane. Learn about this formula and see how it is used to find the midpoint of a line segment.

### 10. What is a Parabola?

A parabola is the U shape that we get when we graph a quadratic equation. We actually see parabolas all over the place in real life. In this lesson, learn where, and the correct vocab to use when talking about them.

### 11. Parabolas in Standard, Intercept, and Vertex Form

By rearranging a quadratic equation, you can end up with an infinite number of ways to express the same thing. Learn about the three main forms of a quadratic and the pros and cons of each.

### 12. How to Graph Cubics, Quartics, Quintics and Beyond

Finding the graph of a polynomial isn't too hard. If you can graph, you already know the major steps! With a couple rules and helpful memorizing tools, you will be graphing polynomials in no time!

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### Other Chapters

Other chapters within the ELM: CSU Math Study Guide course

- ELM Test - Numbers and Data: Basic Arithmetic Calculations
- ELM Test - Numbers and Data: Rational Numbers
- ELM Test - Numbers and Data: Decimals and Percents
- ELM Test - Numbers and Data: Irrational Numbers
- ELM Test - Numbers and Data: Data & Statistics
- ELM Test - Algebra: Basic Expressions
- ELM Test - Algebra: Exponents
- ELM Test - Algebra: Linear Equations & Inequalities
- ELM Test - Algebra: Absolute Value Equations & Inequalities
- ELM Test - Algebra: Polynomials
- ELM Test - Algebra: Rational Expressions
- ELM Test - Geometry: Perimeter, Area & Volume
- ELM Test - Geometry: Properties of Objects
- ELM Test - Geometry: Graphing Basics
- About the ELM Test
- ELM Flashcards