Algebra 1 Assessment Study Guide

Questions and Answers

What describes a linear function?

An arc on the graph

A straight line (correct)

A cubic shape

An exponential curve

What is a quadratic function characterized by?

It has x squared in it.

What type of graph does a quadratic function create?

A parabola

What is the definition of an exponential function?

When there is a variable in the exponent. Signup and view all the answers

What does the term 'cubic' refer to?

A variable being cubed. Signup and view all the answers

What does 4th degree refer to?

x to the 4th degree. Signup and view all the answers

What is absolute value?

Remove the negative sign and think of it as positive. Signup and view all the answers

What do you base the name of a function off of?

The highest exponent. Signup and view all the answers

A negative number can have a square root.

False Signup and view all the answers

What value will any horizontal line always have?

Y value. Signup and view all the answers

What is an asymptote?

Lines that get super close to the graph curve but never touch it. Signup and view all the answers

What is a parent graph?

A graph that is in simplest form. Signup and view all the answers

What is the linear parent graph?

y=x. Signup and view all the answers

What do you get when you solve f(x) = 4x + 5?

y=4x+5. Signup and view all the answers

Dividing by a fraction is the same as which operation?

Multiplying by its reciprocal Signup and view all the answers

What is the result if the exponent is 0?

<ol> <li></li> </ol> Signup and view all the answers

What does the symbol ≤ mean?

Less than or equal to Signup and view all the answers

What does the symbol ≥ signify?

Greater than or equal to Signup and view all the answers

What is the vertex of a parabola?

Where the parabola meets at the bottom (or the top). Signup and view all the answers

What is the slope of a line with a positive slope?

Upward from left to right. Signup and view all the answers

What characterizes a line with an undefined slope?

Vertical line (x value is always the same). Signup and view all the answers

What does an open upward parabola resemble?

Upward facing U. Signup and view all the answers

What does an open downward parabola resemble?

Downward facing U. Signup and view all the answers

A number is a perfect square if...

Its square root is a positive integer. Signup and view all the answers

What are two ways to find a point if you have an equation?

Plug it into the calculator or solve for y. Signup and view all the answers

What steps do you take to find the intersection point where a parabola and line intersect?

(2nd, calc, intersect, use left and right arrow keys, enter three times). Signup and view all the answers

What categories can all lines be put into?

Positive slope, negative slope, 0 slope, and undefined slope. Signup and view all the answers

What categories can all parabolas be grouped into?

Open upward and open downward. Signup and view all the answers

What type of slope does a horizontal line have?

0 slope. Signup and view all the answers

Study Notes

Linear Functions

Linear equations graph as straight lines.
The highest exponent in a linear function is 1.

Quadratic Functions

Quadratic functions include a variable with an exponent of 2.
Graphs of quadratic equations form a parabola, which can open upward or downward.

Exponential Functions

Exponential functions have variables in their exponents.

Cubic and Higher Degree Functions

Cubic functions contain variables raised to the power of 3.
4th degree functions involve variables raised to the power of 4.

Absolute Value

Absolute value represents the distance from zero, disregarding negative signs.

Function Naming

The name of a function is based on the highest exponent present.

Characteristics of Lines

Horizontal lines maintain a constant Y value.
The slope of a horizontal line is 0; vertical lines have an undefined slope.

Asymptotes

Asymptotes are lines that approach a curve without ever touching it.

Irrational Numbers

Irrational numbers have non-repeating, non-terminating decimal expansions, e.g., Euler's number (E=2.71828...).

Function Notation

f(3) indicates substituting X with 3 to find the corresponding Y value.
The equation Y = f(X) shows the relationship between input (X) and output (Y).

Parent Graphs

Parent graphs represent the simplest form of functions.
Examples include linear parent graph (Y = X) and quadratic parent graph (Y = X²).

Algebra Operations

Dividing by a fraction equals multiplying by its reciprocal.
An exponent of 0 results in a value of 1.

Vertex of a Parabola

The vertex is the highest or lowest point of a parabola.

Finding Intersection Points

To determine intersections between a line and a parabola, use a graphing calculator's intersect function.

Classifying Lines and Parabolas

Lines are categorized as positive slope, negative slope, 0 slope, or undefined slope.
Parabolas fall into two categories: open upward or open downward.

Perfect Squares

A number is a perfect square if its square root is a positive integer.

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Description

This quiz focuses on key algebraic concepts including linear, quadratic, exponential, and cubic functions. Each term is defined clearly to help students prepare for assessments in Algebra 1. Use these flashcards to test your understanding and enhance your skills.