Algebra 1 Fall Semester Test Review Part B

Front

What is the formula to calculate the average rate of change of a function?

Back

The average rate of change of a function f(x) over the interval [a, b] is given by the formula: \( \frac{f(b) - f(a)}{b - a} \).

Front

If a river's water level is receding at a rate of 0.5 feet per day, how do you express this as a linear equation?

Back

The equation can be expressed as: \( y = 34 - 0.5x \), where y is the water level and x is the number of days.

Front

What does it mean for a function to be in standard form?

Back

A linear equation is in standard form if it is written as \( Ax + By = C \), where A, B, and C are integers, and A is non-negative.

Front

How do you find the value of a function at a specific point?

Back

To find the value of a function f(x) at a specific point x = a, substitute a into the function: \( f(a) \).

Front

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

Back

The slope-intercept form of a linear equation is given by: \( y = mx + b \), where m is the slope and b is the y-intercept.

Front

How do you calculate the total earnings from multiple jobs with different pay rates?

Back

Total earnings can be calculated using the equation: \( E = 10x + 15y \), where x is the number of lawns raked and y is the number of lawns mowed.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of the function when x = 0.

Front

How do you interpret the slope of a linear function?

Back

The slope represents the rate of change of the function; it indicates how much y changes for a unit change in x.

Front

What is the average growth rate of a tree if it grows from 2 meters to 4 meters over 4 years?

Back

The average growth rate is \( \frac{4 - 2}{4 - 0} = \frac{2}{4} = \frac{1}{2} \) meters per year.

Front

How do you solve for x in a linear equation?

Back

To solve for x, isolate x on one side of the equation using inverse operations.