A day full of math games & activities. Find one near you.

A day full of math games & activities. Find one near you.

A day full of math games & activities. Find one near you.

A day full of math games & activities. Find one near you.

# If f is continuous on (-∞, ∞), what can you say about its graph? (select all that apply.)

The graph of f has a hole.

The graph of f has a jump.

The graph of f has a vertical asymptote.

None of these

**Solution:**

Given that f is continuous in (-∞, ∞)

A graph will have a hole/jump/break only if the function is discontinuous. It is given that f is a continuous function. A continuous function is not necessary to have vertical asymptotes.

For example, if we consider y = x^{3} which is continuous in (-∞, ∞) does not contain any vertical asymptotes whereas when we consider y = tan x it is continuous in its domain and has vertical asymptotes at all odd multiples of π/2.

Therefore, the answer is none of the above.

## If f is continuous on (-∞, ∞), what can you say about its graph? (select all that apply.)

**Summary:**

If f is continuous on (-∞, ∞) it indicates that it doesn't have vertical asymptotes or holes or any jump discontinuity anywhere.

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