Question 1

Which of the following describes the transformation of the graph of $$y = f(x) to$$ $$y = f(x-4) + 2$$?

Accepted Answer

Shift 4 units to the right and 2 units upward

Question 2

Given the function $$y = -f(x)$$, how is its graph related to the graph of $$y = f(x)$$?

Accepted Answer

It is reflected across the x-axis

Question 3

If $$f(x) = x^2$, which of the following is the vertex of the parabola g(x$$) = $$(x-3)^2 + 5$?

Accepted Answer

$$(3, 5)$$

Question 4

Which transformation results in a vertical stretch of the graph of $$y = f(x) by a $$factor of 3?

Accepted Answer

$$y = 3f(x)$$

Question 5

Given $$f(x) = x^2$, which equation represents a reflection of f(x$$)$$ across the y-axis?

Accepted Answer

$$y = f(-x)$$

Question 6

A company’s cost and revenue functions are $$C(x) = 12x + 32$$ and $$R(x) = -4x^2$ + 36x. $$What is the minimum break-even quantity?

Accepted Answer

$$x = 2$$

Question 7

For the quadratic function $$f(x) = ax^2$ + bx + c$$, the vertex $$(h, k)$$ can be found using which formulas?

Accepted Answer

$$h = -\frac{b}{2a},\ k = f(h)$$

Question 8

If $$f(x) = x^2$, which of the following graphs is compressed vertically by a factor of $$\frac{1}{2}$$?

Accepted Answer

$$y = \frac{1}{2}x^2$

Question 9

Given $$f(x) = x^2$, which transformation results in the graph opening downward and shifted 2 units down?

Accepted Answer

$$y = -x^2$ - 2$$

Question 10

Suppose the age at first marriage for women in the US is modeled by $$P(t) = 0.011t^2$ - 0.712t + 20.755$$, where $$t is $$years since 1900. What is the predicted age in 2025?

Accepted Answer

$$29.2$$

Question 11

Which of the following statements is true about the graph of $$y = af(x)$$ compared to $$y = f(x)$$?

Accepted Answer

It is stretched vertically if $$|a| \u003e 1$$

Question 12

Given $$f(x) = x^2$ - 8x + 17$$, rewrite it in vertex form and identify the vertex.

Accepted Answer

Vertex form: $$f(x) = (x-4)^2$ + 1$$, Vertex: $$(4, 1)$$

Question 13

If $$y = \sqrt{x-1}$$, how is this graph related to $$y = \sqrt{x}$$?

Accepted Answer

Shifted 1 unit to the right

Question 14

A parabola has vertex $$(-3, -8)$$ and passes through $$(0, 10). $$What is its equation in the form $$f(x) = a(x-h)^2$ + k$$?

Accepted Answer

$$f(x) = 2(x+3)^2$ - 8$$

Question 15

Given $$C(x) = 12x + 32$$ and $$R(x) = -4x^2$ + 36x$$, what is the maximum profit and at what quantity does it occur?

Accepted Answer

Maximum profit is $$4,000 at$$ $$x = 3$$

Question 16

Which of the following best describes the effect of $$y = f(-x) on $$the graph of $$y = f(x)$$?

Accepted Answer

Reflection across the y-axis

Question 17

If $$f(x) = x^2$, which transformation results in the graph being shifted 5 units upward and reflected across the x-axis?

Accepted Answer

$$y = -x^2$ + 5$$

Question 18

Given the quadratic function $$f(x) = ax^2$ + bx + c$$, what is the axis of symmetry?

Accepted Answer

$$x = -\frac{b}{2a}$$

Question 19

If $$y = f(x+2) - 3$$, how is the graph of $$y = f(x)$$ transformed?

Accepted Answer

Shifted 2 units to the left and 3 units downward

Transformations of Graphs and Quadratic Functions in Business Calculus

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