Limits MC Calculator

The graph of a function f is shown above. Which of the following statements is true?

• f(a) = 2

• f is continuous at x = 2.

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The function f is defined for all x in the closed interval [a,b]. If f does not attain a maximum value on [a,b], which of the following must be true?

• f is not continuous on [a,b].

• f is not bounded on [a,b].

• f does not attain a minimum value on [a,b].

• The graph of f has a vertical asymptote in the interval [a,b].

• The equation f'(x) = 0 does not have a solution in the interval [a,b].

The vertical line x = 2 is an asymptote for the graph of the function f. Which of the following statements must be false?

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If the above is true, then which of the following statements about f must be true?

• f is continuous at x = a.

• f is differentiable at x = a.

• For all values of x, f(x) = f(a).

• The line y = f(a) is tangent to the graph of f at x = a.

• The line x = a is a vertical asymptote of the graph of f.