For problems 1-4 match the blue absolute value function to \( f(x) \) by dragging the vertex A and B, which is a point to the right of A. Once you have successfully matched the function compare it to \( f(x)=|x| \) by checking the box in the lower right. Repeat three times.
Sketch and compare the following functions to the parent function \( f(x) = |x| \):
5) \( g(x)=|x|+2 \)
6) \( h(x)=|x|−3 \)
7) \( k(x)=|x+3| \)
8) \( m(x)=|x−7| \)
9) \( n(x)=-|x|−4 \)
10) \( p(x)=|x+4|−6 \)
11) \( q(x)=|x−2|+5 \)
12) \( r(x)=-\frac{1}{2}|x+2|−3 \)
13) \( s(x)=-3|x+4|+1 \)
14) \( t(x)=\frac{9}{8}|x−10|+2 \)
15) \( v(x)=1.2|x+7| \)
5) \( g(x)=|x|+2 \)
6) \( h(x)=|x|−3 \)
7) \( k(x)=|x+3| \)
8) \( m(x)=|x−7| \)
9) \( n(x)=-|x|−4 \)
10) \( p(x)=|x+4|−6 \)
11) \( q(x)=|x−2|+5 \)
12) \( r(x)=-\frac{1}{2}|x+2|−3 \)
13) \( s(x)=-3|x+4|+1 \)
14) \( t(x)=\frac{9}{8}|x−10|+2 \)
15) \( v(x)=1.2|x+7| \)
Given the description below, write a function that describes the translation from the reference function \( f(x) = |x| \):
16) Shifted to the right seven and up two and opens up.
17) Shifted down five, vertically compressed and opens down.
18) Shifted to the left, vertically stretched and opens up.
19) Opens down, shifted down eight and to the left two.
20) Vertically stretched, opens down, shifted to the left three and up \( 15 \).
16) Shifted to the right seven and up two and opens up.
17) Shifted down five, vertically compressed and opens down.
18) Shifted to the left, vertically stretched and opens up.
19) Opens down, shifted down eight and to the left two.
20) Vertically stretched, opens down, shifted to the left three and up \( 15 \).
Review
Match each system of linear equations with its solution. 21) \( \begin{cases} y = \dfrac{1}{2}x + 5\\x + 4y = 8\\ \end{cases}\) 22) \( \begin{cases} x + 3y = 1\\2x - y = 9\\ \end{cases}\) 23) \( \begin{cases} -2x - 2y = 3\\x = \dfrac{1}{2}y - 1\\ \end{cases}\) 24) \( \begin{cases} 3x = 8y\\x = 6y + 5\\ \end{cases}\) |
A: \(\left(-\dfrac{7}{2}, -5\right)\) B: \((-4, 3)\) C: \(\left(-4, -\dfrac{3}{2}\right)\) D: \((5, -1)\) |