About This Chapter
TACHS: Graphing Functions - Chapter Summary
Before taking the TACHS exam, review the ins and outs of working with functions through these short video lessons. Gain confidence as you rediscover what you may already know and pick up some new information along the way. In these lessons, you will find information on:
- How to graph functions
- Types of functions
- Slope and line intercepts
- The point-slope, distance and mid-point formulas
- Parabola forms
- Graphing cubics, quartics and more
Our lessons are designed to appeal to several learning styles. If you are a visual or audio learner, our short, engaging lessons are for you. If you prefer written text, written transcripts are available. Links between the quizzes and the video lessons make referral back and forth convenient, and our subject-matter experts are available to answer questions if you need help.
TACHS: Graphing Functions Chapter Objectives
There are four subtests that make up the TACHS exam, which is a requirement for admission into many Catholic high schools. You will be tested for your skills in reading, writing, general reasoning and mathematics. This chapter aligns with some of the material in the mathematics subtest.
All of the questions on the TACHS exam are multiple choice. You will take the test using pencil and paper. Each question offers a choice of possible answers and you must select the correct one.
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. 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.
4. 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.
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. 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!
7. 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.
8. 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.
9. 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.
10. 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 within the Test for Admission into Catholic High Schools (TACHS): Practice & Study Guide course
- TACHS: Vocabulary Practice
- TACHS: Reading Comprehension
- TACHS: Reading Interpretation & Analysis
- TACHS: Technical & Informational Text
- TACHS: Literary Text
- TACHS: Poetry
- TACHS: Language & Spelling
- TACHS: Sentence Structure & Word Usage
- TACHS: Expressing Ideas in Writing
- TACHS: Number Sense & Operations
- TACHS: Basic Arithmetic Operations
- TACHS: Integers
- TACHS: Irrational & Rational Numbers
- TACHS: Inequality Practice
- TACHS: Estimation in Mathematics
- TACHS: Decimals
- TACHS: Fractions
- TACHS: Percent
- TACHS: Ratios & Proportion
- TACHS: Basic Algebraic Expressions
- TACHS: Algebraic Distribution
- TACHS: Square Roots
- TACHS: Exponents & Exponential Expressions
- TACHS: Scientific Notation
- TACHS: Standard Measurement
- TACHS: Introduction to Geometry
- TACHS: Geometric Measurement
- TACHS: Symmetry, Similarity & Congruence
- TACHS: Properties of Lines
- TACHS: The Coordinate Graph
- TACHS: Transformations in Math
- TACHS: Triangles
- TACHS: Triangle Theorems & Proofs
- TACHS: The Pythagorean Theorem
- TACHS: Graphical Representations of Data
- TACHS: Statistics & Data Analysis
- TACHS: Probability & Permutations
- TACHS: Properties of Functions
- TACHS: Factoring
- TACHS: Simplifying & Solving Rational Expressions
- TACHS: Linear Equations
- TACHS: Systems of Linear Equations
- TACHS: Mathematical Patterns
- TACHS: Mathematical Reasoning
- TACHS: Reasoning Abilities
- TACHS Flashcards