ALG I Review

Front

What is the average rate of change?

Back

The average rate of change of a function between two points is the change in the function's value divided by the change in the input value. It is calculated as \( \frac{f(b) - f(a)}{b - a} \).

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce. For example, if a function has a minimum value of -5.2, the range is \( y \geq -5.2 \).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry of a quadratic function is a vertical line that divides the graph into two mirror-image halves. It can be found using the formula \( x = -\frac{b}{2a} \) for a quadratic in the form \( ax^2 + bx + c \).

Front

How do you calculate the total cost for hourly services?

Back

To calculate the total cost for hourly services, multiply the hourly rate by the total number of hours worked. For example, if a lawyer charges $120 per hour for 3 hours and 20 minutes, the total cost is $480.

Front

What is the slope of a line?

Back

The slope of a line measures its steepness and direction. It is calculated as \( \frac{\text{rise}}{\text{run}} \), or the change in y over the change in x. A slope of 5 means that for every 1 unit increase in x, y increases by 5 units.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form \( f(x) = ax^2 + bx + c \), where a, b, and c are constants and a ≠ 0.

Front

What are zeros of a function?

Back

Zeros of a function are the values of x for which the function's output is zero. They are the x-intercepts of the graph of the function.

Front

What is the difference between domain and range?

Back

The domain of a function is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values).

Front

How do you find the slope between two points?

Back

To find the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\), use the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form \( f(x) = mx + b \), where m is the slope and b is the y-intercept.