Key Algebra 1 Concepts

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Questions and Answers

What is the independent variable?

The letter that you can control; your input.

What is the dependent variable?

The letter that is by itself; your output.

What is the slope?

Rate of change; rise over run; change in 'y' divided by the change in 'x'.

What is the x-intercept?

Point(s) where a graph crosses the y-axis; ordered pair(s) where the x coordinate is zero. Signup and view all the answers

What is the y-intercept?

Point(s) where a graph crosses the y-axis; ordered pair(s) where the x coordinate is zero. Signup and view all the answers

What is the domain?

The set of independent variables; the 'x's'; read a graph from left to right. Signup and view all the answers

What is the range?

The set of dependent variables; the 'y's'; read a graph from bottom to top. Signup and view all the answers

What is a function?

A graph that passes a vertical line test; a set of ordered pairs in which the 'x's don't repeat. Signup and view all the answers

What is a linear function?

A function (equation) that makes a non-vertical straight line and has a constant rate of change (slope). Signup and view all the answers

What is a quadratic function?

A function or equation involving x. Signup and view all the answers

What is an exponential function?

A function that has a common multiple or divisor between terms. Signup and view all the answers

What is inverse variation?

x * y = a constant value; y = a/x. Signup and view all the answers

What are inequalities?

When solving, if you multiply or divide by a negative, change (flip) the inequality. Signup and view all the answers

What is the distributive property?

The number and the sign in front of a parenthesis must be multiplied by everything inside the parenthesis. Signup and view all the answers

What does value of a function mean?

Means substitute or plug a number in for 'x'. Signup and view all the answers

What are transformations involving y = x^2 + c?

The bigger the 'a' is, the faster the ends of the graph go up or down; the 'c' makes the whole graph go up or down. Signup and view all the answers

What are exponent rules?

When you multiply common variables, add their exponents; when you divide, subtract their exponents. Signup and view all the answers

What does parallel mean in terms of lines?

Lines that have the same slope but different y-intercepts; lines that never intersect. Signup and view all the answers

What does perpendicular mean in terms of lines?

Lines that have opposite reciprocal slopes; lines that intersect at a 90 degree angle. Signup and view all the answers

Study Notes

Key Algebra 1 Concepts

Independent Variable: The controllable input letter in an equation or function.
Dependent Variable: The output letter, which responds to the independent variable.
Slope: Represents the rate of change in a linear relationship; calculated as rise over run, or change in y divided by change in x.
X-intercept: The point(s) where a graph intersects the x-axis; occurs when y equals zero.
Y-intercept: The point(s) where a graph crosses the y-axis; occurs when x equals zero.
Domain: The set of all possible independent variable values (x-values) for a function; read a graph from left to right.
Range: The set of all possible dependent variable values (y-values) for a function; read a graph from bottom to top.
Function: A relationship where each input (x) has a unique output (y); verified by the vertical line test.
Linear Function: A function that graphs as a straight line and has a constant slope.
Quadratic Function: A function involving x, typically represented in a standard form such as ( ax^2 + bx + c ).
Exponential Function: A function where each term represents a constant factor or multiple relative to previous terms.
Inverse Variation: The relationship where the product of two variables equals a constant; mathematically expressed as ( xy = k ) or ( y = \frac{a}{x} ).
Inequalities: Statements that show the relative size or order of two values; multiplying or dividing by a negative number reverses the inequality direction.
Distributive Property: A principle stating that multiplying a term by a sum or difference inside parentheses means applying that term to each element within, e.g., ( a(b+c) = ab + ac ).
Value of a Function: Refers to substituting a specific number into the function’s equation in place of the independent variable.
Transformations of ( y = x^2 + c ): Changes in the graph's shape based on the value of "a" (steeper or wider) and position due to "c" (upward or downward shift).
Exponent Rules:
- Multiplying like bases requires adding exponents.
- Dividing like bases requires subtracting exponents.
- Any variable raised to the zero power equals one.
- When raising a power to another power, multiply the exponents.
Parallel Lines: Lines that run in the same direction, having identical slopes yet differing y-intercepts; they never meet.
Perpendicular Lines: Lines that intersect at a right angle (90 degrees); their slopes are opposite reciprocals of one another.

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Description

This quiz covers fundamental concepts in Algebra 1, including independent and dependent variables, slope, intercepts, domain, and range. Test your understanding of these essential terms and their relationships within linear functions. It's perfect for high school students looking to solidify their algebra knowledge.