Chapter 12

For each pair of functions, find a) \((f+g)(x)\) b) \((f+g)(5), \text { c) }(f-g)(x), \text { and } \mathrm{d})(f-g)(2)\) $$f(x)=-3 x+1, g(x)=2 x-11$$

Let \(f(x)=a x^{2}+b x+c .\) How do you know if the function has a maximum or minimum value at the vertex?

If \(z\) varies directly as \(y,\) then as \(y\) increases, the value of \(z=\)_________

Graph each function by plotting points, and identify the domain and range. $$f(x)=|x|+3$$

For each pair of functions, find a) \((f+g)(x)\) b) \((f+g)(5), \text { c) }(f-g)(x), \text { and } \mathrm{d})(f-g)(2)\) $$f(x)=5 x-9, g(x)=x+4$$

Is there a maximum value of the function \(y=2 x^{2}+12 x+11 ?\) Explain your answer.

Graph each function by plotting points, and identify the domain and range. $$g(x)=|x-2|$$

If \(a\) varies inversely as \(b\), then as \(b\) increases, the value of \(a\)_________

Given a quadratic function of the form \(f(x)=a(x-h)^{2}+k,\) answer the following. What is the equation of the axis of symmetry?

What is the domain of a relation?

For each pair of functions, find a) \((f+g)(x)\) b) \((f+g)(5), \text { c) }(f-g)(x), \text { and } \mathrm{d})(f-g)(2)\) $$f(x)=4 x^{2}-7 x-1, g(x)=x^{2}+3 x-6$$

Graph each function by plotting points, and identify the domain and range. $$k(x)=\frac{1}{2}|x|$$

a) Does the function attain a minimum or maximum value at its vertex? b) Find the vertex of the graph of \(f(x)\) c) What is the minimum or maximum value of the function? d) Graph the function to verify parts a) \(-c\) ). $$f(x)=x^{2}+6 x+9$$

Decide whether each equation represents direct, inverse, joint, or combined variation. $$y=6 x$$

Given a quadratic function of the form \(f(x)=a(x-h)^{2}+k,\) answer the following. How do you know if the parabola opens upward?

Identify the domain and range of each relation, and determine whether each relation is a function. $$\\{(5,0),(6,1),(14,3),(14,-3)\\}$$

For each pair of functions, find a) \((f+g)(x)\) b) \((f+g)(5), \text { c) }(f-g)(x), \text { and } \mathrm{d})(f-g)(2)\) $$f(x)=-2 x^{2}+x+8, g(x)=3 x^{2}-4 x-6$$

Graph each function by plotting points, and identify the domain and range. $$g(x)=2|x|$$

a) Does the function attain a minimum or maximum value at its vertex? b) Find the vertex of the graph of \(f(x)\) c) What is the minimum or maximum value of the function? d) Graph the function to verify parts a) \(-c\) ). $$f(x)=-x^{2}+2 x+4$$

Decide whether each equation represents direct, inverse, joint, or combined variation. $$c=4 a b$$

Given a quadratic function of the form \(f(x)=a(x-h)^{2}+k,\) answer the following. How do you know if the parabola opens downward?

Identify the domain and range of each relation, and determine whether each relation is a function. $$\\{(-5,7),(-4,5),(0,-3),(0.5,-4),(3,-9)\\}$$

For each pair of functions, find a) \((f g)(x)\) and \(b\) ) \((f g)(-3)\). $$f(x)=x, g(x)=-x+5$$

Graph each function by plotting points, and identify the domain and range. $$g(x)=x^{2}-4$$

a) Does the function attain a minimum or maximum value at its vertex? b) Find the vertex of the graph of \(f(x)\) c) What is the minimum or maximum value of the function? d) Graph the function to verify parts a) \(-c\) ). $$f(x)=-\frac{1}{2} x^{2}+4 x-6$$

Given a quadratic function of the form \(f(x)=a(x-h)^{2}+k,\) answer the following. How do you know if the parabola is narrower than the graph of \(y=x^{2} ?\)

For each pair of functions, find a) \((f g)(x)\) and \(b\) ) \((f g)(-3)\). $$f(x)=-2 x, g(x)=3 x+1$$

Graph each function by plotting points, and identify the domain and range. $$h(x)=(x-2)^{2}$$

Decide whether each equation represents direct, inverse, joint, or combined variation. $$z=3 \sqrt{x}$$

Given a quadratic function of the form \(f(x)=a(x-h)^{2}+k,\) answer the following. How do you know if the parabola is wider than the graph of \(y=x^{2} ?\)

For each pair of functions, find a) \((f g)(x)\) and \(b\) ) \((f g)(-3)\). $$f(x)=2 x+3, g(x)=3 x+1$$

Solve. An object is fired upward from the ground so that its height \(h\) (in feet) \(t\) sec after being fired is given by \(h(t)=-16 t^{2}+320 t\) a) How long does it take the object to reach its maximum height? b) What is the maximum height attained by the object? c) How long does it take the object to hit the ground?

Graph each function by plotting points, and identify the domain and range. $$f(x)=-x^{2}-1$$

For quadratic function, identify the vertex, axis of symmetry, and \(x\)- and \(y\)-intercepts. Then, graph the function. \(f(x)=(x+1)^{2}-4\)

For each pair of functions, find a) \((f g)(x)\) and \(b\) ) \((f g)(-3)\). $$f(x)=4 x+7, g(x)=x-5$$

Graph each function by plotting points, and identify the domain and range. $$f(x)=(x-2)^{2}-5$$

Solve. An object is thrown upward from a height of \(64 \mathrm{ft}\) so that its height \(h\) (in feet) \(t\) sec after being thrown is given by $$h(t)=-16 t^{2}+48 t+64$$ a) How long does it take the object to reach its maximum height? b) What is the maximum height attained by the object? c) How long does it take the object to hit the ground?

For quadratic function, identify the vertex, axis of symmetry, and \(x\)- and \(y\)-intercepts. Then, graph the function. \(g(x)=(x-3)^{2}-1\)

For each pair of functions, find a) \(\left(\frac{f}{g}\right)(x)\) and b \(\left(\frac{f}{g}\right)(-2)\) Identify any values that are not in the domain of \(\left(\frac{f}{g}\right)(x)\) $$f(x)=6 x+9, g(x)=x+4$$

Graph each function by plotting points, and identify the domain and range. $$f(x)=\sqrt{x+3}$$

Write a general variation equation using \(k\) as the constant of variation. \(M\) varies directly as \(n\)

For quadratic function, identify the vertex, axis of symmetry, and \(x\)- and \(y\)-intercepts. Then, graph the function. \(g(x)=(x-2)^{2}+3\)

For each pair of functions, find a) \(\left(\frac{f}{g}\right)(x)\) and b \(\left(\frac{f}{g}\right)(-2)\) Identify any values that are not in the domain of \(\left(\frac{f}{g}\right)(x)\). $$f(x)=3 x-8, g(x)=x-1$$

Graph each function by plotting points, and identify the domain and range.$$g(x)=\sqrt{x}+2$$

Solve. The average number of traffic tickets issued in a city on any given day Sunday - Saturday can be approximated by $$T(x)=-7 x^{2}+70 x+43$$ where \(x\) represents the number of days after Sunday \((x=0 \text { represents Sunday, } x=1\) represents Monday, etc.), and \(T(x)\) represents the number of traffic tickets issued. On which day are the most tickets written? How many tickets are issued on that day?

Write a general variation equation using \(k\) as the constant of variation. \(q\) varies directly as \(r\)

For quadratic function, identify the vertex, axis of symmetry, and \(x\)- and \(y\)-intercepts. Then, graph the function. \(h(x)=(x+2)^{2}+7\)

Determine whether each relation describes \(y\) as a function of \(x\) $$y=4 x^{2}-10 x+3$$

For each pair of functions, find a) \(\left(\frac{f}{g}\right)(x)\) and b \(\left(\frac{f}{g}\right)(-2)\) Identify any values that are not in the domain of \(\left(\frac{f}{g}\right)(x)\). $$f(x)=x^{2}-5 x-24, g(x)=x-8$$

Graph each function by plotting points, and identify the domain and range. $$f(x)=2 \sqrt{x}$$