For problems 1-4 write down the function below. Drag the blue point that is on the vertex of the blue absolute value function to match the red equation below. Sketch the correct graph. Repeat three times.
For problems 5-8 try to match the red function to the pink one shown by manipulating the numerator and denominator sliders on the right. Sketch the function and the equation when it matches. Repeat three times.
Graph the function below using a 10 by 10 axis. Make sure to label the vertex. Is the function increasing or decreasing in \( 3 \leq x \leq 6 \)? State the domain and range.
9) \( f(x)=|x+3| \)
10) \( g(x)=|x|+3 \)
11) \( h(x)=-2|x−1| \)
12) \( j(x)=\frac{1}{3}|x|−1 \)
13) \( k(x)=|x+3|−1 \)
14) \( m(x)=2|x−2|+3 \)
Given the graph, write an equation for the absolute value function. State the domain and range.
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Review
How many solutions does each system of linear equations have?
21) \( \begin{cases} 8x - 2y= 12\\-4x + y = -6\\ \end{cases}\)
22) \( \begin{cases} 5x - 3y = -6\\y = -\dfrac{5}{3}x - 3\\ \end{cases}\)
23) \( \begin{cases} -2x + y = 7\\2x + y = 11\\ \end{cases}\)
24) Write a system of linear equations that has infinite solutions.
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