Question 1

Which of the following graphs represents the function $$f(x) = x^2$?

Accepted Answer

The graph that is a parabola opening upwards with its vertex at the origin.

Question 2

Given the function $$f(x) = \sqrt{x}$$, which graph best represents its behavior?

Accepted Answer

The graph that starts at the origin and increases slowly, only defined for $$x \geq 0.$$

Question 3

Which graph corresponds to the function $$f(x) = |x|$$?

Accepted Answer

The graph that forms a 'V' shape with its vertex at the origin.

Question 4

Which graph represents the reciprocal function $$f(x) = \frac{1}{x}$$?

Accepted Answer

The graph with two branches, one in the first quadrant and one in the third quadrant, both approaching the axes but never touching them.

Question 5

Which graph best represents the function $$f(x) = x^3$?

Accepted Answer

The graph that passes through the origin, increases rapidly for positive $$x$$, and decreases rapidly for negative $$x.$$

Question 6

Which graph corresponds to the function $$f(x) = \ln(x)$$?

Accepted Answer

The graph that is only defined for $$x \u003e 0$$, passes through $$(1, 0)$$, and increases slowly as $$x$$ increases.

Question 7

Which graph represents the constant function $$f(x) = 5$$?

Accepted Answer

The graph that is a horizontal line at $$y = 5.$$

Question 8

Which graph best represents the function $$f(x) = \sqrt[3]{x}$$?

Accepted Answer

The graph that passes through the origin, increases for positive $$x$$, and decreases for negative $$x$$, but is defined for all real $$x.$$

Question 9

Which graph corresponds to the function $$f(x) = x$$?

Accepted Answer

The graph that is a straight line passing through the origin with a slope of 1.

Question 10

Which graph represents the function $$f(x) = x^2$ - 4$$?

Accepted Answer

The graph that is a parabola opening upwards, shifted down by 4 units.

Library of Functions: Fundamental Graphs and Their Properties

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