About This Chapter
Graphing Functions Overview - Chapter Summary
The Graphing Functions Overview chapter will boost your understanding of this subject. See information on the use of point-slope formula for the equation of a line, exponentials and the simplifying of polynomials functions, and vertical and horizontal asymptotes. More lesson topics cover:
- Basic functions and graphs
- Finding and applying the intercepts of lines
- How to graph zero slope, undefined slope and more
- Graphing functions of functions and compounding functions
- Properties and factoring of polynomials functions
- Logarithms, the natural log and exponentials
- Tangents and slopes on a graph
- Implicit functions
This chapter consists of short videos. There is an accompanying video transcript and keyword-based timeline tool for your convenience. We include a self-assessment quiz for you to check your understanding of the material as you progress through your studies.
1. Graphing Basic Functions
Graphs are just like maps - when you know the language! Review how locations have x and y coordinates similar to latitude and longitude, and how to plot points in the Cartesian plane.
2. 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.
3. 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.
4. 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!
5. 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.
6. Compounding Functions and Graphing Functions of Functions
We know that functions map numbers to other numbers, so what happens when you have a function of a function? Welcome to functions within functions, the realm of composite functions!
7. Understanding and Graphing the Inverse Function
If you use a function to map a to b, is there a way to go back from b to a again? Learn how to find and graph inverse functions so that you can turn a into b and back into a.
8. Polynomial Functions: Properties and Factoring
Everything from projectile motion to trigonometric functions can be described by polynomials. Review factoring, polynomials and quadratic functions in this lesson.
9. Polynomial Functions: Exponentials and Simplifying
How do we keep track of a rapidly multiplying population of bunnies? Well, those are simply powers of 2. Review powers and simplify problems with exponents in this lesson.
10. Exponentials, Logarithms & the Natural Log
Use the properties of exponentials and logarithms to learn how carbon dating works. This lesson covers properties of a natural log and rules of logarithms.
11. Slopes and Tangents on a Graph
Hit the slopes and learn how the steepness of a line is calculated. Calculate the slopes between points and draw the tangents of curves on graphs in this lesson.
12. Implicit Functions
Sometimes inputting a variable into a function 'black box' doesn't yield a simple output. Find out what happens when you can't isolate the dependent variable on one side of the equal sign.
13. Horizontal and Vertical Asymptotes
No matter how hard you try to get to them, asymptotes remain out of reach. Learn about these invisible lines on graphs that show you places your equations just can't go.
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Other chapters within the STAAR Algebra II: Test Prep & Practice course
- Complex and Imaginary Numbers
- Calculating & Simplifying Exponential Expressions
- Understanding Polynomial Functions
- Solving Algebraic Equations Overview
- Operations with Radical Expressions
- The Basics of Functions
- Solving & Graphing Systems of Equations
- Solving & Graphing 1 & 2 Variable Inequalities
- Solving & Graphing Quadratics
- Quadratics & Higher Order Polynomials
- Solving Exponential & Logarithmic Functions
- Absolute Value Equations
- Rational Functions & Expressions
- About the STARR Tests
- STAAR Algebra II Flashcards