Algebra EOC (all topics)

Front

What is a horizontal shift in a graph?

Back

A horizontal shift occurs when the graph of a function is moved left or right along the x-axis. For example, the function g(x) = (x - 7.5)² is a horizontal shift of f(x) = x² to the right by 7.5 units.

Front

What is standard linear form?

Back

Standard linear form of a linear equation is expressed as Ax + By = C, where A, B, and C are constants, and A and B are not both zero.

Front

How do you evaluate a function at a specific value?

Back

To evaluate a function at a specific value, substitute the value into the function's equation and simplify. For example, p(x) = 5(x² + 1) + 16, to find p(11), substitute 11 for x.

Front

What is the value of g(x) = x³ + 9 when x = -2?

Back

g(-2) = (-2)³ + 9 = -8 + 9 = 1.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For example, the domain of the function defined by the interval (-2, 3] includes all x-values greater than -2 and up to 3.

Front

What does it mean to transform a function?

Back

Transforming a function involves changing its position or shape on the graph through shifts, stretches, or reflections.

Front

What is a vertical shift in a graph?

Back

A vertical shift occurs when the graph of a function is moved up or down along the y-axis. For example, g(x) = x² + 5 is a vertical shift of f(x) = x² up by 5 units.

Front

What is the difference between a horizontal and vertical shift?

Back

A horizontal shift moves the graph left or right, while a vertical shift moves it up or down.

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

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.