Question 1

Given the graph of the parabola with vertex at $$(0, 2)$$ and passing through the point $$(1, 7)$$, what is the equation of the parabola in the form $$y = a(x - h)^2$ + k$$?

Accepted Answer

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

Question 2

Which of the following graphs represents a one-to-one function?

Accepted Answer

Graph A

Question 3

Based on the tide graph, during which intervals is the water level increasing?

Accepted Answer

$$[0, 2.6]$$, $$[8.7, 14.8]$$, $$[20.9, 27]$$

Question 4

Given the graph of a cubic polynomial with a local minimum at $$x \approx -2$$ and a local maximum at $$x \approx 2$$, which of the following statements is true?

Accepted Answer

The minimum degree of the polynomial is 4.

Question 5

For the rational function shown, which of the following statements is true?

Accepted Answer

The function contains a vertical asymptote at $$x = -3.$$

Question 6

Given the graph of a quartic polynomial with two local maxima and one local minimum, which of the following is true?

Accepted Answer

The minimum degree of the polynomial is 4.

Question 7

Which graph best represents exponential growth?

Accepted Answer

Graph 1 (curve increasing faster as $$t$$ increases)

Question 8

Which graph best represents logarithmic growth?

Accepted Answer

Graph 2 (curve increasing but leveling off)

Question 9

Which graph best represents a linear relationship?

Accepted Answer

Graph 3 (straight line)

Question 10

Which graph best represents a quadratic function?

Accepted Answer

Graph 6 (parabola opening upwards)

Question 11

Which graph best represents the function $$y = \frac{1}{x}$$?

Accepted Answer

Graph 7 (hyperbola with two branches in opposite quadrants)

College Algebra Study Guidance: Graphs, Functions, and Equations

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