Algebra Support Winter Final Exam Study Guide

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form C(x) = mx + b, where m is the slope and b is the y-intercept.

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How do you formulate a linear function for a real-world scenario?

Back

Identify the fixed cost and the variable cost per unit. For example, if a company charges a fixed fee plus a variable fee per minute, the function can be expressed as C(x) = variable_cost * x + fixed_cost.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function. In the context of a cost function, it indicates how much the cost increases for each additional unit of usage.

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What is the y-intercept in a linear function?

Back

The y-intercept is the value of the function when x = 0. It represents the starting value or fixed cost in a real-world scenario.

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How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using algebraic operations such as addition, subtraction, multiplication, or division.

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What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the inequalities overlap on a graph.

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How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What is a line of best fit?

Back

A line of best fit is a straight line that best represents the data on a scatter plot. It minimizes the distance between the line and all data points.

Front

What does it mean for a function to be decreasing?

Back

A decreasing function is one where the output value decreases as the input value increases. This is indicated by a negative slope.

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How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the variable into the function and simplify.