Q: Jimmy’s Music Shop has cost function $$C(x) = 77x + 1900$$ and revenue function $$R(x) = 146x. $$What is the profit from selling $$x = 80$$ keyboards?

$$P(80) = 146 \times 80 - (77 \times 80 + 1900)$$

Q: If $$\lim_{x \to -4} H(x)$$ exists and $$H(-4)$$ exists, which of the following is necessary for $$H to be $$continuous at $$x = -4$$?

$$\lim_{x \to -4} H(x) = H(-4)$$

Q: If $$f is $$continuous at $$x = -10$$, which of the following must be true?

$$\lim_{x \to -10} f(x) = f(-10)$$

Question 1

Which of the following equations represents a function?

Accepted Answer

$$y = x^2$ - 8x + 7$$

Question 2

Given $$f(x) = x^2$ - 8x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$(4, -9)$$

Question 3

Find the domain of the function $$f(x) = \frac{x-2}{6x-12}.$$

Accepted Answer

Question 4

If $$\lim_{x 	o a} f(x)$$ exists, which of the following must be true?

Accepted Answer

$$f(x)$$ approaches a finite value as $$x$$ approaches $$a$$

Question 5

An investor puts $9900 into an account that pays 9% interest compounded continuously. How much will be in the account after 4 years?

Accepted Answer

$$9900 	imes e$$^{0.36}$$

Question 6

Let $$f(x) = 2x^2$ - 9x + 79. $$What is $$f'(x)$$?

Accepted Answer

$$4x - 9$$

Question 7

Given $$f(x) = 3x^2$ - 9x - 66$$, find the equation of the tangent line to $$f(x) at $$the point $$(6, -12).$$

Accepted Answer

Question 8

Jimmy’s Music Shop has cost function $$C(x) = 77x + 1900$$ and revenue function $$R(x) = 146x. $$What is the profit from selling $$x = 80$$ keyboards?

Accepted Answer

$$P(80) = 146 	imes 80 - (77 	imes 80 + 1900)$$

Question 9

Given $$P(t) = 0.6t^2$ + 0.4t + 75$$, where $$t is $$the number of years since 2010, what is the average rate of change of the poster price between 2015 and 2024?

Accepted Answer

$$\frac{P(14) - P(5)}{14 - 5}$$

Question 10

If $$\lim_{x 	o -4} H(x)$$ exists and $$H(-4)$$ exists, which of the following is necessary for $$H to be $$continuous at $$x = -4$$?

Accepted Answer

$$\lim_{x 	o -4} H(x) = H(-4)$$

Question 11

For the function $$f(x) = x^2$ - 8x + 7$$, what is the line of symmetry?

Accepted Answer

$$x = 4$$

Question 12

Given $$\lim_{x 	o \infty} \frac{5x^2$ - 9x + 8}{4x^2$ - 8x + 1}$$, what is the value of the limit?

Accepted Answer

$$\frac{5}{4}$$

Question 13

If $$f is $$continuous at $$x = -10$$, which of the following must be true?

Accepted Answer

$$\lim_{x 	o -10} f(x) = f(-10)$$

Question 14

For the function $$f(x) = x^2$ - 8x + 7$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 1$$ and $$x = 7$$

Question 15

If $$f(x) is $$continuous at $$x = 2$$, which of the following is true?

Accepted Answer

$$\lim_{x 	o 2} f(x) = f(2)$$

Question 16

Given $$C(x) = 77x + 1900$$ and $$R(x) = 146x$$, what is the average unit profit function $$F(x)$$?

Accepted Answer

$$F(x) = \frac{R(x) - C(x)}{x}$$

Question 17

If $$\lim_{x 	o a} f(x) = f(a)$$, which of the following is true?

Accepted Answer

$$f(x) is $$continuous at $$x = a$$

Question 18

Let $$f(x) = 2x^2$ - 9x + 79. $$What is the value of $$f'(2)$$?

Accepted Answer

Business Calculus: Functions, Limits, Continuity, and Applications

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