Question

The graph shows the reciprocal parent function.

Which statement is true?


A. The function has no intercepts.

B. (1,1) is the x- and y-intercept of the function.

C. (0,0) is the x- and y-intercept of the function.

D. (0,1) is the x- and y-intercept of the function.
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Answer 1

I think the answer is C

Answer 2

The reciprocal parent function has no intercepts.

To determine the x- and y-intercepts of the reciprocal parent function, let's first recall what the reciprocal function looks like.

The reciprocal function is defined as f(x) = 1/x.

The x-intercept occurs when y = 0, which means we need to find the value of x when f(x) = 0.

However, there is no value of x that makes the reciprocal of zero equal to zero.

Therefore, the function has no x-intercept.

On the other hand, the y-intercept occurs when x = 0, which means we need to find the value of y when f(0) = 1/0.

However, division by zero is undefined in mathematics, so the reciprocal parent function does not have a y-intercept.

Therefore, the correct statement is A. The function has no intercepts.