Explain how the graph of $y=-f(x-2)$ compares to the graph of $y=f(x)$.

Height of a projectile. An object is projected vertically upward from the top of a building with an initial velocity of $144 \mathrm{ft} / \mathrm{sec}$. Its distance $s(t)$ in feet above the ground after $t$ seconds is given by the equation

$$s(t)=-16 t^2+144 t+100 .$$

Find the height of the building.

Find an equation of the circle that satisfies the stated conditions.

Center $C(-3,6)$, tangent to the $y$-axis

Find the domain $D$ and range $R$ of $f$.

$$f(x)=\sqrt{x+4}$$

Height of a projectile. An object is projected vertically upward from the top of a building with an initial velocity of $144 \mathrm{ft} / \mathrm{sec}$. Its distance $s(t)$ in feet above the ground after $t$ seconds is given by the equation

$$s(t)=-16 t^2+144 t+100 .$$

Find its maximum distance above the ground.

Use the slope-intercept form to find the slope and $\boldsymbol{y}$-intercept of the given line, and sketch its graph.

$$2 x=15-3 y$$

Sketch the graph of $f$.

$$f(x)=\sqrt{x+4}$$

If $f$ is an odd function and $g$ is an even function, is $f g$ even, odd, or neither even nor odd?

Find the intervals on which $f$ is increasing, is decreasing, or is constant.

$$f(x)=x^2-1$$

Gasoline mileage. The number of miles $M$ that a certain automobile can travel on one gallon of gasoline at a speed of $v \mathrm{mi} / \mathrm{hr}$ is given by

$$M=-\frac{1}{30} v^2+\frac{5}{2} v \quad \text { for } 0<v<70 .$$

(a) Find the most economical speed for a trip.

(b) Find the largest value of $M$.

Find the domain $D$ and range $R$ of $f$.

$$f(x)=x^2-1$$

Sketch the line through $A$ and $B$, and find its slope $m$.

$$A(4,-3), \quad B(4,2)$$

If $S(r)=4 \pi r^2$ and $D(t)=2 t+5$, find $(S \circ D)(t)$.

Find an equation of the circle that satisfies the stated conditions.

Center at the origin, passing through $P(4,-7)$