Exam 2: Functions and Graphs

Evaluate the piecewise function at the given value of the independent variable. - $h ( x ) = \left\{ \begin{array} { l l } \frac { x ^ { 2 } - 7 } { x + 6 } & \text { if } x \neq - 6 \\ x - 2 & \text { if } x = - 6 \end{array} ; h ( - 6 ) \right.$

Based on the graph, find the range of y = f(x). - $f(x)=\left\{\begin{array}{ll}4 & \text { if }-6 \leq x<-2 \\|x| & \text { if }-2 \leq x<8 \\\sqrt{x} & \text { if } 8 \leq x \leq 13\end{array}\right.$

Evaluate the function at the given value of the independent variable and simplify. - $f ( x ) = x ^ { 2 } - 3 ; \quad f ( x - 4 )$

Identify the intervals where the function is changing as requested. -Constant

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph of f. - $(x)=\sqrt{x}, g(x)=\sqrt{x}-2$

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph of f. - $f(x)=x^{3}, g(x)=x^{3}+2$

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph of f. - $f(x)=|x|, g(x)=|x|-4$

Give the domain and range of the relation. -{(10, -3), (12, 3), (-8, -7), (6, -1)}

Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph of f. - $(x)=-2 x, g(x)=-2 x-3$

Identify the intercepts -

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x. -

Find the slope of the line that goes through the given points. -(2, -3), (-7, 8)

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x. -

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x. -

Based on the graph, find the range of y = f(x). - $f(x)=\left\{\begin{array}{ll}-\frac{1}{2} x & \text { if } x \neq 0 \\-7 & \text { if } x=0\end{array}\right.$

Use the graph to find the indicated function value. -y = f(x). Find f(3).

Determine whether the equation defines y as a function of x. - $x + y ^ { 3 } = 27$

Use the graph of the given function to find any relative maxima and relative minima. - $f(x)=x^{3}-12 x+2$

Write the word or phrase that best completes each statement or answers the question. -The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce $W ( t ) = \left\{ \begin{array} { l l } t & \text { if } 0 \leq v < 1.79 \\33 - \frac { ( 10.45 + 10 \sqrt { v } - v ) ( 33 - t ) } { 22.04 } & \text { if } 1.79 \leq v < 20 \\33 - 1.5958 ( 33 - t ) & \text { if } v \geq 20\end{array} \right.$ where v represents the wind speed (in meters per second)and t represents the air temperature (°C). Compute the wind chill for an air temperature of 15°C and a wind speed of 12 meters per second. (Round the answer to one decimal place.)

Evaluate the piecewise function at the given value of the independent variable. - $(x)=\left\{\begin{array}{ll}x+1 & \text { if } x<1 \\3 & \text { if } x \geq 1\end{array}\right.$