Algebra Midterm Exam Review

Front

What is the vertical line test?

Back

A method to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, it is not a function.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be expressed in the form f(x) = mx + b, where m and b are constants.

Front

How do you determine if a relation is a function?

Back

A relation is a function if each input (x-value) has exactly one output (y-value).

Front

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

Back

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

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, indicating the value of f(0).

Front

How do you solve the inequality 10(x + 3) ≤ 50?

Back

First, simplify to x + 3 ≤ 5, then subtract 3 to find x ≤ 2.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c.

Front

How do you evaluate a function at a specific point, such as f(-3) for f(x) = 2x² + 7?

Back

Substitute -3 into the function: f(-3) = 2(-3)² + 7 = 18 + 7 = 25.

Front

What does it mean for a function to be non-linear?

Back

A function is non-linear if it cannot be represented by a straight line on a graph, often involving exponents or other operations.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input.