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Chapter 2: Q11. (page 93)

Graph each function. Identify the domain and range.

h(x)={x+3鈥�if鈥�x鈮�鈭�12x鈥�if鈥�x>鈭�1

Short Answer

Expert verified

The domain is all real numbers.

The range is all real numbers.

Step by step solution

01

Step-1 – Range and Domain

The domain of the function is the set of all input values and range of the function is the set of all output values.

02

Step-2 – Draw the graph.

The given function is h(x)={x+3鈥夆赌�if鈥夆赌�x鈮�鈭�12x鈥夆赌夆�夆赌�if鈥夆赌�x>鈭�1

The graph of the equation h(x)=x+3is linear equation for x鈮�-1.

Here, -1satisfies the inequalityx鈮�-1. Therefore, end with a closed circle at x=-1.

The graph of the equation h(x)=2xis linear function for x>-1.

Here, -1not satisfies the inequalityx>-1. Therefore, start with an open circle at x=-1.

03

Step-3 – Determine the domain and range.

The domain is all real numbers.

The range is all real numbers.

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Most popular questions from this chapter

In an election, a total of 4000 votes were cast for three candidates, A, B and C. Candidate C received 800 votes. If candidate B received more votes than candidate C and candidate A received more votes than candidate B, what is the least number of votes that candidate A could have received?

Solve each inequality.

-2<3x+1<7

Find the slope of the line that passes through each pair of points

鈥�鈥�(-2,5),(4,5)

Graph each equation or inequality

h鈥�(x)=x+2ifx<鈭�22x鈭�1ifx鈮�鈭�2

State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.

19.g(x)=10+2x2
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