Solution Bank Equations and Inequalities Target B
Answers to the Practice Problems are below in random order.
\(\begin{align}&\text{No Solution}\ & \ \ \ \ \ &\text{No Solution} \ & \ \ \ \ \ &\text{No Solution}\\\\
&(-2,-3)\ \text{and}\ (6,-1)\ & \ \ \ \ \ &x = 1\ \text{and}\ x = 0\ & \ \ \ \ \ & x = 1\\\\
&y=-\frac{3}{2}\left|x-4\right|+5\ & \ \ \ \ \ &x = -2\ \text{and}\ x = 10 \ & \ \ \ \ \ & x=-\frac{1}{3}\ \text{and}\ x = 2\\\\
&x = -3\ \text{and}\ x = -1\ & \ \ \ \ \ & y=3\left|x+4\right|-5\ & \ \ \ \ \ &\text{An absolute value equation cannot equal a negative value.}\end{align}\)
\(\begin{align}&r(x)\ \text{is vertically stretched by a factor of 8 and translated left 2 units and down 4 units}\\\\
&\text{ Vertex: (-3,-1), AoS: x=-3, Domain:}\ \{x|x \in \Re\}\ \text{or}\ (-\infty,\infty), \text{Range:}\ \{y|y \le-1\}\ \text{or}\ (-\infty,-1]\\\\&\text{ Vertex: (5,0), AoS: x=5, Domain:}\ \{x|x \in \Re\}\ \text{or}\ (-\infty,\infty), \text{Range:}\ \{y|y \ge0\}\ \text{or}\ [0,\infty )\\\\
&\text{w(x) is reflected in the x-axis, vertically compressed by a factor of}\ \frac{1}{2}, \text{and translated up 3 units}\end{align}\)
Answers to the Practice Problems are below in random order.
\(\begin{align}&\text{No Solution}\ & \ \ \ \ \ &\text{No Solution} \ & \ \ \ \ \ &\text{No Solution}\\\\
&(-2,-3)\ \text{and}\ (6,-1)\ & \ \ \ \ \ &x = 1\ \text{and}\ x = 0\ & \ \ \ \ \ & x = 1\\\\
&y=-\frac{3}{2}\left|x-4\right|+5\ & \ \ \ \ \ &x = -2\ \text{and}\ x = 10 \ & \ \ \ \ \ & x=-\frac{1}{3}\ \text{and}\ x = 2\\\\
&x = -3\ \text{and}\ x = -1\ & \ \ \ \ \ & y=3\left|x+4\right|-5\ & \ \ \ \ \ &\text{An absolute value equation cannot equal a negative value.}\end{align}\)
\(\begin{align}&r(x)\ \text{is vertically stretched by a factor of 8 and translated left 2 units and down 4 units}\\\\
&\text{ Vertex: (-3,-1), AoS: x=-3, Domain:}\ \{x|x \in \Re\}\ \text{or}\ (-\infty,\infty), \text{Range:}\ \{y|y \le-1\}\ \text{or}\ (-\infty,-1]\\\\&\text{ Vertex: (5,0), AoS: x=5, Domain:}\ \{x|x \in \Re\}\ \text{or}\ (-\infty,\infty), \text{Range:}\ \{y|y \ge0\}\ \text{or}\ [0,\infty )\\\\
&\text{w(x) is reflected in the x-axis, vertically compressed by a factor of}\ \frac{1}{2}, \text{and translated up 3 units}\end{align}\)
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