Chapter 9

Translate each statement of variation into an equation, and use \(k\) as the constant of variation. \(y\) varies inversely as the square of \(x\).

Determine \((f \circ g)(x)\) and \((g \circ f)(x)\) for each pair of functions. Also specify the domain of \((f \circ g)(x)\) and \((g \circ f)(x)\). (Objective 1\()\) \(f(x)=3 x\) and \(g(x)=5 x-1\)

Specify the domain and the range for each relation. Also state whether or not the relation is a function. $$\\{(1,5),(2,8),(3,11),(4,14)\\}$$

Translate each statement of variation into an equation, and use \(k\) as the constant of variation. \(y\) varies directly as the cube of \(x\).

Determine \((f \circ g)(x)\) and \((g \circ f)(x)\) for each pair of functions. Also specify the domain of \((f \circ g)(x)\) and \((g \circ f)(x)\). (Objective 1\()\) \(f(x)=4 x-3\) and \(g(x)=-2 x\)

Graph each of the following linear and quadratic functions. $$f(x)=3 x+3$$

Specify the domain and the range for each relation. Also state whether or not the relation is a function. $$\\{(0,0),(2,10),(4,20),(6,30),(8,40)\\}$$

Translate each statement of variation into an equation, and use \(k\) as the constant of variation. \(C\) varies directly as \(g\) and inversely as the cube of \(t\).

Determine \((f \circ g)(x)\) and \((g \circ f)(x)\) for each pair of functions. Also specify the domain of \((f \circ g)(x)\) and \((g \circ f)(x)\). (Objective 1\()\) \(f(x)=-2 x+1\) and \(g(x)=7 x+4\)

Graph each of the following linear and quadratic functions. $$f(x)=-2 x^{2}$$

Specify the domain and the range for each relation. Also state whether or not the relation is a function. $$\\{(0,5),(0,-5),(1,2 \sqrt{6}),(1,-2 \sqrt{6})\\}$$

Translate each statement of variation into an equation, and use \(k\) as the constant of variation. \(V\) varies jointly as \(l\) and \(w\).

Determine \((f \circ g)(x)\) and \((g \circ f)(x)\) for each pair of functions. Also specify the domain of \((f \circ g)(x)\) and \((g \circ f)(x)\). (Objective 1\()\) \(f(x)=6 x-5\) and \(g(x)=-x+6\)

Graph each of the following linear and quadratic functions. $$f(x)=-4 x^{2}$$

Specify the domain and the range for each relation. Also state whether or not the relation is a function. $$\\{(1,1),(1,2),(1,-1),(1,-2),(1,3)\\}$$

Translate each statement of variation into an equation, and use \(k\) as the constant of variation. The volume \((V)\) of a sphere is directly proportional to the cube of its radius \((r)\).

Determine \((f \circ g)(x)\) and \((g \circ f)(x)\) for each pair of functions. Also specify the domain of \((f \circ g)(x)\) and \((g \circ f)(x)\). (Objective 1\()\) \(f(x)=3 x+2\) and \(g(x)=x^{2}+3\)

Graph each of the following linear and quadratic functions. $$f(x)=-3 x$$

Specify the domain and the range for each relation. Also state whether or not the relation is a function. $$\\{(1,2),(2,5),(3,10),(4,17),(5,26)\\}$$

Translate each statement of variation into an equation, and use \(k\) as the constant of variation. At a constant temperature, the volume \((V)\) of a gas varies inversely as the pressure \((P)\).

Determine \((f \circ g)(x)\) and \((g \circ f)(x)\) for each pair of functions. Also specify the domain of \((f \circ g)(x)\) and \((g \circ f)(x)\). (Objective 1\()\) \(f(x)=-2 x+4\) and \(g(x)=2 x^{2}-1\)

Graph each of the following linear and quadratic functions. $$f(x)=-4 x$$

Specify the domain and the range for each relation. Also state whether or not the relation is a function. $$\\{(-1,5),(0,1),(1,-3),(2,-7)\\}$$

Translate each statement of variation into an equation, and use \(k\) as the constant of variation. The surface area \((S)\) of a cube varies directly as the square of the length of an edge \((e)\).

Determine \((f \circ g)(x)\) and \((g \circ f)(x)\) for each pair of functions. Also specify the domain of \((f \circ g)(x)\) and \((g \circ f)(x)\). (Objective 1\()\) \(f(x)=2 x^{2}-x+2\) and \(g(x)=-x+3\)

Graph each of the functions. $$f(x)=x^{3}-2$$

Graph each of the following linear and quadratic functions. $$f(x)=-(x+1)^{2}-2$$

Specify the domain and the range for each relation. Also state whether or not the relation is a function. $$\\{(x, y) \mid 5 x-2 y=6\\}$$

Translate each statement of variation into an equation, and use \(k\) as the constant of variation. The intensity of illumination \((I)\) received from a source of light is inversely proportional to the square of the distance \((d)\) from the source.

Determine \((f \circ g)(x)\) and \((g \circ f)(x)\) for each pair of functions. Also specify the domain of \((f \circ g)(x)\) and \((g \circ f)(x)\). (Objective 1\()\) \(f(x)=3 x^{2}-2 x-4\) and \(g(x)=-2 x+1\)

Graph each of the functions. $$f(x)=|x|+3$$

Graph each of the following linear and quadratic functions. $$f(x)=-(x-2)^{2}+4$$

Specify the domain and the range for each relation. Also state whether or not the relation is a function. $$\\{(x, y) \mid y=-3 x\\}$$

Translate each statement of variation into an equation, and use \(k\) as the constant of variation. The volume \((V)\) of a cone varies jointly as its height and the square of its radius.

Determine \((f \circ g)(x)\) and \((g \circ f)(x)\) for each pair of functions. Also specify the domain of \((f \circ g)(x)\) and \((g \circ f)(x)\). (Objective 1\()\) \(f(x)=\frac{3}{x}\) and \(g(x)=4 x-9\)

Graph each of the functions. $$f(x)=\sqrt{x}+3$$

Graph each of the following linear and quadratic functions. $$f(x)=-x+3$$

Specify the domain and the range for each relation. Also state whether or not the relation is a function. $$\left\\{(x, y) \mid x^{2}=y^{3}\right\\}$$

Translate each statement of variation into an equation, and use \(k\) as the constant of variation. The volume \((V)\) of a gas varies directly as the absolute temperature \((T)\) and inversely as the pressure \((P)\).

Determine \((f \circ g)(x)\) and \((g \circ f)(x)\) for each pair of functions. Also specify the domain of \((f \circ g)(x)\) and \((g \circ f)(x)\). (Objective 1\()\) \(f(x)=-\frac{2}{x}\) and \(g(x)=-3 x+6\)

Graph each of the functions. $$f(x)=\frac{1}{x}-2$$

Graph each of the following linear and quadratic functions. $$f(x)=-2 x-4$$

Specify the domain and the range for each relation. Also state whether or not the relation is a function. $$\left\\{(x, y) \mid x^{2}-y^{2}=16\right\\}$$

Find the constant of variation for each of the stated conditions. \(y\) varies directly as \(x\), and \(y=8\) when \(x=12\).

Determine \((f \circ g)(x)\) and \((g \circ f)(x)\) for each pair of functions. Also specify the domain of \((f \circ g)(x)\) and \((g \circ f)(x)\). (Objective 1\()\) \(f(x)=\sqrt{x+1}\) and \(g(x)=5 x+3\)

Graph each of the functions. $$f(x)=\sqrt{x+3}$$

Graph each of the following linear and quadratic functions. $$f(x)=x^{2}+2 x-2$$

Specify the domain for each of the functions. $$f(x)=7 x-2$$

Find the constant of variation for each of the stated conditions. \(y\) varies directly as \(x\), and \(y=60\) when \(x=24\).

Determine \((f \circ g)(x)\) and \((g \circ f)(x)\) for each pair of functions. Also specify the domain of \((f \circ g)(x)\) and \((g \circ f)(x)\). (Objective 1\()\) \(f(x)=7 x-2\) and \(g(x)=\sqrt{2 x-1}\)