Absolute Value And Step Functions Common Core Algebra 1 Homework Answers

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Absolute Value And Step Functions Common Core Algebra 1 Homework Answers

If you are looking for absolute value and step functions common core algebra 1 homework answers, you have come to the right place. In this article, we will explain what absolute value and step functions are, how to graph them, and how to solve problems involving them. We will also provide you with some examples and practice questions that you can use to test your understanding.

What are absolute value and step functions?

Absolute value and step functions are two types of functions that are often used in algebra. A function is a rule that assigns an output value to every input value. A function can be represented by an equation, a table, a graph, or a verbal description.

Absolute Value And Step Functions Common Core Algebra 1 Homework Answers

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An absolute value function is a function that takes the absolute value of the input. The absolute value of a number is its distance from zero on the number line. For example, the absolute value of -5 is 5, because -5 is 5 units away from zero. The absolute value of 3 is 3, because 3 is 3 units away from zero. The absolute value function can be written as f(x) = x, where x is the input and f(x) is the output.

A step function is a function that has a constant output value for each interval of the input. For example, a step function can be used to model a postage rate that charges $0.55 for the first ounce and $0.15 for each additional ounce. The step function can be written as f(x) = 0.55 + 0.15âxâ, where x is the input in ounces and f(x) is the output in dollars. The symbol âxâ means the greatest integer less than or equal to x. For example, â3.2â = 3 and â-1.7â = -2.

How to graph absolute value and step functions?

To graph an absolute value function, we can use the following steps:

• Identify the vertex of the graph, which is the point where the function changes direction. The vertex has the coordinates (h,k), where h is the value of x that makes the expression inside the absolute value zero, and k is the value of f(x) when x = h.

• Plot the vertex on the coordinate plane.

• Draw two rays that start from the vertex and form a V-shape. The rays should have a slope of either 1 or -1, depending on whether the function opens up or down.

• Extend the rays until they reach the edges of the graph.

To graph a step function, we can use the following steps:

• Identify the intervals of the input and the corresponding output values. For each interval, we can write an inequality that describes the range of x values and an equation that gives the output value.

• Plot a point for each output value on the coordinate plane.

• Draw horizontal line segments that connect the points within each interval.

• Draw open circles at the endpoints of each interval to indicate that they are not included in the function.

How to solve problems involving absolute value and step functions?

To solve problems involving absolute value and step functions, we can use different methods depending on the type of problem. Here are some common types of problems and how to approach them:

• If we are given an equation involving an absolute value function and asked to find its solutions, we can use the property that x = a if and only if x = a or x = -a. For example, to solve x - 2 = 4, we can write ea27c8ed11