Question 1

Given the points $$(-1, 0), (0, -3), (1, 0), (2, 3), (3, 6)$$, determine whether the function is linear or nonlinear. If linear, find the slope.

Accepted Answer

Nonlinear

Question 2

Suppose the supply and demand for smoothies at a festival are given by $$S(p) = -150 + 40p$$ and $$D(p) = 600 - 70p. $$What is the equilibrium price?

Accepted Answer

$$p = 5$$

Question 3

For the same supply and demand functions, what is the equilibrium quantity?

Accepted Answer

$$Q = 200$$

Question 4

If the price of a smoothie is $6, is there a surplus or shortage, and by how much?

Accepted Answer

Surplus of 70 smoothies

Question 5

Find the price that produces a shortage of 100 smoothies using $$S(p) = -150 + 40p$$ and $$D(p) = 600 - 70p.$$

Accepted Answer

$$p = 6$$

Question 6

A semicircle of radius $$r = 23x - 5 is $$inscribed in a rectangle so that the diameter is the length of the rectangle. Express the area $$A of $$the rectangle as a function of $$x.$$

Accepted Answer

$$A(x) = (23x - 5)^2$

Question 7

A right triangle has one vertex at the origin, one at $$(x, y) on$$ $$y = 27x^3$, x$$ \u003e 0$$, and one on the positive y$-axis. Express the area A$ of the triangle as a function of x$.

Accepted Answer

$$A(x) = \frac{1}{2} x \cdot 27x^3$

Question 8

An island is 11 miles from the nearest point $$P on a $$straight shoreline. A town is 19 miles down the shore from $$P. If a $$person can row at 6 mph and walk at 3 mph, express the total travel time $$T(x) as a $$function of $$x$$, the distance from $$P to $$where the person lands.

Accepted Answer

$$T(x) = \frac{\sqrt{11^2$ + x^2$}}{6} + \frac{19 - x}{3}$$

Question 9

For the travel time function $$T(x) = \frac{\sqrt{11^2$ + x^2$}}{6} + \frac{19 - x}{3}$$, what is the domain?

Accepted Answer

$$0 \leq x \leq 19$$

Question 10

If the person lands the boat 8 miles from $$P$$, how long will it take to reach the town? (Round to the nearest tenth)

Accepted Answer

About 5.1 hours

Question 11

A parcel-shipping service charges $$C(w) = 2.00(w - 5)$$ for packages over 5 pounds. What is the domain of this function?

Accepted Answer

$$w \u003e 5$$

Question 12

If someone ships a 12-pound package, what is the shipping cost?

Accepted Answer

$$14.00$$

Question 13

Given the function $$y = x^2$ - 8x + 20$$, what is the vertex?

Accepted Answer

$$(4, 4)$$

Question 14

For the function $$y = x^2$ - 8x + 20$$, what is the axis of symmetry?

Accepted Answer

$$x = 4$$

Question 15

Which transformation describes $$y = -2(x + 1)^3$ - 3$$ compared to $$y = x^3$?

Accepted Answer

Reflect over $$x-$$axis, vertical stretch by 2, left 1, down 3

Question 16

What is the $$y-$$intercept of $$y = x^2$ - 8x + 20$$?

Accepted Answer

$$(0, 20)$$

Question 17

Which of the following best describes the domain of $$f(x) = \sqrt{x - 4}$$?

Accepted Answer

$$[4, \infty)$$

Question 18

If $$f(x) = 3x^2$, which transformation results in g(x) = 3(x$$ - $$2)^2 + 5$?

Accepted Answer

Shift right 2, up 5

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