Algebra 1 Midterm Review

Front

What is the range of a mapping?

Back

The range of a mapping is the set of all possible output values (y-values) that result from applying the function to its domain.

Front

Back

The solution to the equation is x = 30.

Front

How do you find the rate of change?

Back

The rate of change is found by dividing the change in the dependent variable by the change in the independent variable. For example, if Jack is 43 feet away after 5 seconds and 58 feet away after 10 seconds, the rate of change is (58 - 43) / (10 - 5) = 3 feet per second.

Front

If Mrs. Taylor was 10 feet off the ground at 0 seconds and 20 feet at 5 seconds, what is her rate in feet per second?

Back

Her rate is 2 feet per second, calculated as (20 - 10) / (5 - 0).

Front

Write an equation for the caterer charging $100 for 10 people and $175 for 25 people.

Back

The equation is y = 5x + 50, where y is the total cost and x is the number of people.

Front

What is a function in mathematics?

Back

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

Front

Define 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.

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 calculate the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does it mean for an equation to have no solution?

Back

An equation has no solution when there are no values that satisfy the equation, often resulting in a contradiction.