This is an example of the golden ratio, or phi, a proportionality constant that appears in nature. The numerical approximate value of phi is 1.618. From www.goldenratio.net.

$Human Anatomy$. Each section of your index finger, from the tip to the base of the wrist, is larger than the preceding one by about the golden (Fibonacci) ratio. Find an equation that represents the ratio of each section of your finger related to the previous one if one section is eight units long and the next section is five units long.

Find the average rate of change of $f(x)=|2 x-1|$ from $x=1$ to $x=5$.

Solve the radical equation for the given variable.

$$\sqrt{25-x^2}=x+1$$

Specify any values that must be excluded from the solution set and then solve.

$$\frac{4}{x+1}-\frac{8}{x-1}=3$$

Evaluate the given quantities applying the following four functions.

$$f(x)=2 x-3 \quad F(t)=4-t^2 \quad g(t)=5+t \quad G(x)=x^2+2 x-7$$

$$f(-2)$$

Write the equation in slope-intercept form. Identify the slope and the $y$-intercept.

$$\frac{1}{4} x+\frac{2}{5} y=2$$

Evaluate $f(g(1))$ and $g(f(2))$, if possible.

$$f(x)=\sqrt{1-x}, \quad g(x)=x^2+2$$

Solve by completing the square.

$$2 p^2+8 p=-3$$

Use the given graph to sketch the graph of the indicated functions.

$$y=\frac{1}{2} F(x-1)+2$$

This is an example of the golden ratio, or phi, a proportionality constant that appears in nature. The numerical approximate value of phi is 1.618. From www.goldenratio.net.

$Human Anatomy$. The length of your forearm $F$ (wrist to elbow) is directly proportional to the length of your hand $H$ (length from wrist to tip of middle finger). Write the equation that describes this relationship if the length of your forearm is 11 inches and the length of your hand is $6.8$ inches.

Solve the radical equation $3 x-6 \sqrt{x-1}=3$ for the given variable.

Solve the polynomial inequality and express the solution set in interval notation.

$$x^2-4 x<6$$

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for each function.

$$f(x)=x^2-3 x+2$$

Write the equation in slope-intercept form. Identify the slope and the $y$-intercept.

$$\frac{1}{2} x+\frac{2}{3} y=4$$