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In this lesson, we will learn how to analyze a piecewise-defined function, graph it, find its domain and range, and write the equation that represents it from its graph.

Q1:

Determine the domain of the function represented by the given graph.

Q2:

Q3:

Find the range of the function.

Q4:

Determine the range of the function represented by the following graph.

Q5:

Find the domain of the real function

Q6:

Q7:

Give the piecewise definition of the function 𝑓 whose graph is shown.

Q8:

Give the piecewise definition of the function ℎ whose graph is shown.

Q9:

Give the piecewise definition of the function 𝑝 whose graph is shown.

Q10:

Q11:

The graph of the function 𝑓 is formed of a ray with slope − 3 from the point ( − 1 , 2 ) , a line segment between the points ( − 1 , 2 ) and ( 2 , 1 ) , and a ray with slope 7 from the point ( 2 , 1 ) . Write the function in the form 𝑓 ( 𝑥 ) = 𝑎 + 𝑏 𝑥 + 𝑐 | 𝑥 + 1 | + 𝑑 | 𝑥 − 2 | , where 𝑎 , 𝑏 , 𝑐 , 𝑑 a n d are numbers that you should find.

Q12:

Give the piecewise definition of the function 𝑔 whose graph is shown.

Q13:

The graph in figure (i) is of 𝑓 ( 𝑥 ) = 5 2 | 𝑥 | + 1 2 𝑥 , which could also be written as follows

Find the values of 𝑎 and 𝑏 that would make graph (ii) that of 𝑔 ( 𝑥 ) = 𝑎 | 𝑥 − 5 | + 𝑏 ( 𝑥 − 5 ) .

Q14:

Write an equation for each part of the domains 𝑥 ≤ 1 and 𝑥 > 1 of the piecewise-defined function shown in the graph.

Q15:

Write an equation for each part of the domains − 8 ≤ 𝑥 ≤ − 2 , − 2 < 𝑥 < 2 , 2 ≤ 𝑥 < 8 , and 8 ≤ 𝑥 ≤ 1 0 of the piecewise-defined function shown in the graph.

Q16:

Which of the following is the function whose graph is shown?

Q17:

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