Algebra Semester Review

Front

What is the range of a graph?

Back

The range of a graph is the set of all possible output values (y-values) that a function can produce. For example, if the range is -3 ≤ y < 1, it means y can take any value from -3 to just below 1.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means that one line's slope is the negative reciprocal of the other's.

Front

What is the process to simplify the expression (3x^2)(3x^4y^3)?

Back

To simplify, multiply the coefficients (3 * 3 = 9) and add the exponents of like bases: x^(2+4) = x^6. The simplified expression is 9x^6y^3.

Front

How do you solve the equation 2(2x + 3) = -6(x + 9)?

Back

First, distribute: 4x + 6 = -6x - 54. Then, combine like terms: 10x = -60. Finally, divide by 10: x = -6.

Front

What is the equation of a line that is perpendicular to y = 1/3x - 7?

Back

The slope of the given line is 1/3. The slope of the perpendicular line is -3. Using the point (1, -1), the equation is y = -3x + 2.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

Front

What is the difference between independent and dependent variables?

Back

The independent variable is the input of a function (often x), while the dependent variable is the output (often y) that depends on the input.

Front

What does it mean to factor an expression?

Back

Factoring an expression means rewriting it as a product of its factors. For example, x^2 - 9 can be factored as (x - 3)(x + 3).