Solving Absolute Value Equations
1) Explain why \(\left|9x+14\right|=-10\) has no solution.
For problems 2-8 solve the absolute value equations.
2) \(\left|6x-5\right|=7\)
3) \(\frac{1}{2}\left|x-4\right|+2=5\)
4) \(-3\left|2x+4\right|+1=5\)
5) \(\frac{3}{5}\left|x-6\right|+12=9\)
6) \(2\left|3x-1\right|+4=2x+6\)
7) \(\left|4x+5\right|=-5x+14\)
8) \(\left|5x-2\right|=3x-10\)
Graphing Absolute Value Equations
For problems 9-10 describe the transformations from the parent function \(f\left(x\right)=\left|x\right|\).
9) \(w\left(x\right)=-\frac{1}{2}\left|x\right|+3\)
10) \(r\left(x\right)=8\left|x+2\right|-4\)
For problems 11-13 graph the absolute value functions. State the vertex, axis of symmetry, domain and range of the translated function.
11) \(h\left(x\right)=\frac{1}{3}\left|x-5\right|\)
12) \(g\left(x\right)=-2\left|x+3\right|-1\)
13) Find the point(s) of intersection of the functions \(p\left(x\right)=-\left|x-3\right|+2\) and \(n\left(x\right)=\frac{1}{2}\left|x\right|-4\).
For problems 14-15 write the equation of the absolute value functions graphed below.
14)
15)