Chapter 5

Write an equation of a line passing through the point (-2,5) and parallel to the line \(3 x-4 y+12=0\).

The vertices of a triangle are \(A(-2,0), B(0,6),\) and \(C(4,0) .\) Find an equation of a line containing the median from vertex \(A\) to \(\overline{B C}\).

Write an equation of a circle whose center is at (2,-3) and tangent to the line \(y=-1\)

Solve the inequality \(|6-3 x|<18\) and sketch the solution on the real number line.

Given \(f(x)=x^{2}+3 x,\) find \(\frac{f(x+h)-f(x)}{h}\) in simplest form.

Determine which of the following equations represent \(y\) as a function of \(x\) : (1) \(x y=-8\) (2) \(4 x^{2}+9 y^{2}=36\) (3) \(3 x^{2}-y=1\) (4) \(y^{2}-x^{2}=4\)

If \(f(x)=x^{2}\) and \(g(x)=\sqrt{25-x^{2}},\) find \((f \circ g)(x)\) and indicate its domain.

Find the inverse of the function \(f(x)=x^{3}+1\).

Sketch the graph of the equation \(y=3 \cos \left(\frac{1}{2} x\right)\) in the interval \(-2 \pi \leq x \leq 2 \pi\) and indicate the amplitude, frequency, and period.

On the same set of axes, sketch the graphs of: (1) \(y=\ln x\) (2) \(y=\ln (-x)\) (3) \(y=-\ln (x+3)\)

Solve the inequality \(|2 x+4| \leq 10\).

On the same set of axes, sketch the graphs of: (1) \(y=\ln x\) (2) \(y=\ln (-x)\) (3) \(y=-\ln (x+3)\)

Evaluate \(\tan \left(\arccos \frac{\sqrt{2}}{2}\right)\).

Solve for \(x\) to the nearest thousandth: \(e^{2 x}-6 e^{x}+5=0\).

Solve for \(x\) to the nearest thousandth: \(3 \ln 2 x-3=12\).

Solve the inequality \(\frac{2 x-1}{x+1} \leq 1\).

Determine if the function \(f(x)=-2 x^{4}+x^{2}+5\) is even, odd, or neither.

Given the function \(f(x)=x^{4}-4 x^{3},\) determine the intervals over which the function is increasing, decreasing, or constant. Find all zeros of \(f(x),\) and indicate any relative minimum and maximum values of the function.

Given a linear function \(y=f(x)\), with \(f(2)=4\) and \(f(-4)=10,\) find \(f(x)\).

Solve the inequality \(x^{3}-x \geq 0\) graphically.

If \(f(x)=\frac{1}{x}, x \neq 0,\) evaluate \(\frac{f(x+h)-f(x)}{h}\) and express the answer in simplest form.

Given \(g(x)=3 x-12,\) find \(g^{-1}(3)\).

Write an equation of the tangent line to the graph of \(x^{2}+y^{2}=25\) at the point (4,-3)