Chapter 2

Let \(f(x)=x^{2}\) and \(g(x)=2 x-5 .\) Match each function in Group I with the correct expression in Group II. $$I$$ $$(f+g)(x)$$ $$\mathbf{II}$$ $$A.\quad4 x^{2}-20 x+25$$ $$B.\quad x^{2}-2 x+5$$ $$C.\quad 2 x^{2}-5$$ $$D.\quad \frac{x^{2}}{2 x-5}$$ $$E. \quad x^{2}+2 x-5$$ $$F. \quad 2 x^{3}-5 x^{2}$$

Write an equation in \(x\) and \(y\) that results in the desired transformation. Do not use a calculator. The squaring function, vertically stretched by applying a factor of 2

Fill in each blank with the correct response. The domain and the range of the identity function are both _____.

Let \(f(x)=x^{2}\) and \(g(x)=2 x-5 .\) Match each function in Group I with the correct expression in Group II. $$I$$ $$(f-g)(x)$$ $$\mathbf{II}$$ $$A.\quad4 x^{2}-20 x+25$$ $$B.\quad x^{2}-2 x+5$$ $$C.\quad 2 x^{2}-5$$ $$D.\quad \frac{x^{2}}{2 x-5}$$ $$E. \quad x^{2}+2 x-5$$ $$F. \quad 2 x^{3}-5 x^{2}$$

Write an equation in \(x\) and \(y\) that results in the desired transformation. Do not use a calculator. The cubing function, vertically shrunk by applying a factor of \(\frac{1}{2}\)

Fill in each blank with the correct response. The domain of the squaring function is _____, and it's rage is ______.

Let \(f(x)=x^{2}\) and \(g(x)=2 x-5 .\) Match each function in Group I with the correct expression in Group II. $$I$$ $$(f g)(x)$$ $$\mathbf{II}$$ $$A.\quad4 x^{2}-20 x+25$$ $$B.\quad x^{2}-2 x+5$$ $$C.\quad 2 x^{2}-5$$ $$D.\quad \frac{x^{2}}{2 x-5}$$ $$E. \quad x^{2}+2 x-5$$ $$F. \quad 2 x^{3}-5 x^{2}$$

Write an equation in \(x\) and \(y\) that results in the desired transformation. Do not use a calculator. The square root function, reflected across the \(y\) -axis

Let \(f(x)=x^{2}\) and \(g(x)=2 x-5 .\) Match each function in Group I with the correct expression in Group II. $$I$$ $$\left(\frac{f}{g}\right)(x)$$ $$\mathbf{II}$$ $$A.\quad4 x^{2}-20 x+25$$ $$B.\quad x^{2}-2 x+5$$ $$C.\quad 2 x^{2}-5$$ $$D.\quad \frac{x^{2}}{2 x-5}$$ $$E. \quad x^{2}+2 x-5$$ $$F. \quad 2 x^{3}-5 x^{2}$$

Write an equation in \(x\) and \(y\) that results in the desired transformation. Do not use a calculator. The cube root function, reflected across the \(x\) -axis

Fill in each blank with the correct response. The domain of the square root function is _____, and its range is ____.

Let \(f(x)=x^{2}\) and \(g(x)=2 x-5 .\) Match each function in Group I with the correct expression in Group $I$$$I$$$$(f \circ g)(x)$$$$\mathbf{II}$$$$A.\quad4 x^{2}-20 x+25$$$$B.\quad x^{2}-2 x+5$$$$C.\quad 2 x^{2}-5$$$$D.\quad \frac{x^{2}}{2 x-5}$$$$E. \quad x^{2}+2 x-5$$$$F. \quad 2 x^{3}-5 x^{2}$$

For each piecewise-defined function, find (a) \(f(-5),\) (b) \(f(-1)\) (c) \(f(0),\) and (d) \(f(3) .\) Do not use a calculator. $$f(x)=\left\\{\begin{array}{ll} 2 x & \text { if } x \leq-1 \\ x-1 & \text { if } x>-1 \end{array}\right.$$

Write an equation in \(x\) and \(y\) that results in the desired transformation. Do not use a calculator. The absolute value function, vertically stretched by applying a factor of 3 and reflected across the \(x\) -axis

Let \(f(x)=x^{2}\) and \(g(x)=2 x-5 .\) Match each function in Group I with the correct expression in Group $I$$$I$$$$(g \circ f)(x)$$ $$\mathbf{II}$$$$A.\quad4 x^{2}-20 x+25$$$$B.\quad x^{2}-2 x+5$$$$C.\quad 2 x^{2}-5$$$$D.\quad \frac{x^{2}}{2 x-5}$$$$E. \quad x^{2}+2 x-5$$$$F. \quad 2 x^{3}-5 x^{2}$$

For each piecewise-defined function, find (a) \(f(-5),\) (b) \(f(-1)\) (c) \(f(0),\) and (d) \(f(3) .\) Do not use a calculator. $$f(x)=\left\\{\begin{array}{ll} x-2 & \text { if } x<3 \\ 5-x & \text { if } x \geq 3 \end{array}\right.$$

Fill in each blank with the correct response. The largest open interval that the absolute value function decreases on is ____ and the largest open interval that it increases on is _____.

Write an equation in \(x\) and \(y\) that results in the desired transformation. Do not use a calculator. The absolute value function, vertically shrunk by applying a factor of \(\frac{1}{3}\) and reflected across the \(y\) -axis

Let \(f(x)=x^{2}+3 x\) and \(g(x)=2 x-1 .\) Perform the composition or operation indicated. $$(f \circ g)(3)$$

For each piecewise-defined function, find (a) \(f(-5),\) (b) \(f(-1)\) (c) \(f(0),\) and (d) \(f(3) .\) Do not use a calculator. $$f(x)=\left\\{\begin{array}{ll} 2+x & \text { if } x<-4 \\ -x & \text { if }-4 \leq x \leq 2 \\ 3 x & \text { if } x>2 \end{array}\right.$$

The graph of the relation \(x=y^{2}\) is symmetric with respect to the _____.

Write an equation in \(x\) and \(y\) that results in the desired transformation. Do not use a calculator. The cubing function, vertically shrunk by applying a factor of 0.25 and reflected across the \(y\) -axis

Let \(f(x)=x^{2}+3 x\) and \(g(x)=2 x-1 .\) Perform the composition or operation indicated. $$(g \circ f)(-2)$$

For each piecewise-defined function, find (a) \(f(-5),\) (b) \(f(-1)\) (c) \(f(0),\) and (d) \(f(3) .\) Do not use a calculator. $$f(x)=\left\\{\begin{array}{ll} -2 x & \text { if } x<-3 \\ 3 x-1 & \text { if }-3 \leq x \leq 2 \\ -4 x & \text { if } x>2 \end{array}\right.$$

Fill in each blank with the correct response. The function \(f(x)=x^{4}+x^{2}\) is an \(\overline {(even/odd)}\) function.

Write an equation in \(x\) and \(y\) that results in the desired transformation. Do not use a calculator. The square root function, vertically shrunk by applying a factor of 0.2 and reflected across the \(x\) -axis

Let \(f(x)=x^{2}+3 x\) and \(g(x)=2 x-1 .\) Perform the composition or operation indicated. $$(f \circ g)(x)$$

Graph each piece wise-defined function. Is \(f\) continuous on its entire domain? Do not use a calculator. $$f(x)=\left\\{\begin{array}{ll} x-1 & \text { if } x \leq 3 \\ 2 & \text { if } x>3 \end{array}\right.$$

Fill in each blank with the correct response. The function \(f(x)=x^{3}+x\) is an \(\overline {(even/oddd)}\) function.

Use transformations of graphs to sketch the graphs of \(y_{1}, y_{2},\) and \(y_{3}\) by hand. Check by graphing in an appropriate viewing window of your calculator. $$y_{1}=x, \quad y_{2}=x+3, \quad y_{3}=x-3$$

Write an equation in \(x\) and \(y\) that results in the desired translation. Do not use a calculator. The squaring function, shifted 2 units downward and 3 units to the right

Let \(f(x)=x^{2}+3 x\) and \(g(x)=2 x-1 .\) Perform the composition or operation indicated. $$(g \circ f)(x)$$

Graph each piece wise-defined function. Is \(f\) continuous on its entire domain? Do not use a calculator. $$f(x)=\left\\{\begin{array}{ll} 6-x & \text { if } x \leq 3 \\ 3 x-6 & \text { if } x>3 \end{array}\right.$$

Fill in each blank with the correct response. If a function is even, its graph is symmetric with respect to the _____, If it is odd, its graph is symmetric with _____ respect to the ____.

Use transformations of graphs to sketch the graphs of \(y_{1}, y_{2},\) and \(y_{3}\) by hand. Check by graphing in an appropriate viewing window of your calculator. $$y_{1}=x^{3}, \quad y_{2}=x^{3}+4, \quad y_{3}=x^{3}-4$$

Write an equation in \(x\) and \(y\) that results in the desired translation. Do not use a calculator. The squaring function, shifted 4 units upward and 1 unit to the left

Let \(f(x)=x^{2}+3 x\) and \(g(x)=2 x-1 .\) Perform the composition or operation indicated. $$(f+g)(3)$$

Graph each piece wise-defined function. Is \(f\) continuous on its entire domain? Do not use a calculator. $$f(x)=\left\\{\begin{array}{ll} 4-x & \text { if } x<2 \\ 1+2 x & \text { if } x \geq 2 \end{array}\right.$$

Give a short answer to each question. If \(f(a)=-5,\) what is the value of \(|f(a)| ?\)

Use transformations of graphs to sketch the graphs of \(y_{1}, y_{2},\) and \(y_{3}\) by hand. Check by graphing in an appropriate viewing window of your calculator. $$y_{1}=|x|, \quad y_{2}=|x-3|, \quad y_{3}=|x+3|$$

Write an equation in \(x\) and \(y\) that results in the desired translation. Do not use a calculator. The square root function, shifted 3 units upward and 6 units to the left

Let \(f(x)=x^{2}+3 x\) and \(g(x)=2 x-1 .\) Perform the composition or operation indicated. $$(f+g)(-5)$$

Graph each piece wise-defined function. Is \(f\) continuous on its entire domain? Do not use a calculator. $$f(x)=\left\\{\begin{array}{ll} 2 x+1 & \text { if } x \geq 0 \\ x & \text { if } x<0 \end{array}\right.$$

Give a short answer to each question. How does the graph of \(f(x)=x^{2}\) compare with the graph of \(f(x)=\left|x^{2}\right| ?\)

Use transformations of graphs to sketch the graphs of \(y_{1}, y_{2},\) and \(y_{3}\) by hand. Check by graphing in an appropriate viewing window of your calculator. $$y_{1}=|x|, \quad y_{2}=|x|-3, \quad y_{3}=|x|+3$$

Write an equation in \(x\) and \(y\) that results in the desired translation. Do not use a calculator. The absolute value function, shifted 1 unit downward and 5 units to the right

Let \(f(x)=x^{2}+3 x\) and \(g(x)=2 x-1 .\) Perform the composition or operation indicated. $$(f g)(4)$$

Graph each piece wise-defined function. Is \(f\) continuous on its entire domain? Do not use a calculator. $$f(x)=\left\\{\begin{array}{ll} 2+x & \text { if } x<-4 \\ -x & \text { if }-4 \leq x \leq 5 \\ 3 x & \text { if } x>5 \end{array}\right.$$

Use transformations of graphs to sketch the graphs of \(y_{1}, y_{2},\) and \(y_{3}\) by hand. Check by graphing in an appropriate viewing window of your calculator. $$y_{1}=\sqrt{x}, \quad y_{2}=\sqrt{x+6}, \quad y_{3}=\sqrt{x-6}$$

Write an equation in \(x\) and \(y\) that results in the desired translation. Do not use a calculator. The squaring function, shifted 2000 units to the right and 500 units upward