Question

Given the graph below, which of the following statements is true?

Answer 1

To be a function, it has to pass the vertical line test, which means a vertical line drawn anywhere in the graph should cut the graph only once, not more.

To be a one-to-one function, it has to pass the vertical line test as well as the horizontal line test, which means that a horizontal line drawn anywhere in the graph should cut the graph only once, not more.

Of course, it passes the vertical line test, so its a function.

Does it pass the horizontal line test? NO! As shown in the attached picture, the blue line (horizontal line) cuts the graph at 3 places. We therefore eliminate choices A and B. We can eliminate choice C because nowhere is it required a function to pass through the origin for it to be one-to-one. Hence, the answer is D (blue line shows this).

ANSWER: D

Answer 2

The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.Option (d) is correct.

Further explanation:

The output values of the function are known as range and the input values on which function is defined is known as the domain of the function.

Given:

The options area as follows,

(a). The graph represents a one-to-one function because every x-value is paired with only one y-value.

(b). The graph represents a one-to-one function because it is defined for all x-values.

(c). The graph does not represent a one-to-one function because it does not pass through the origin.

(d). The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.

Explanation:

The one-to-one function is a function in which every value of the range has exactly one pre-image in the domain.

One-to-one function always passes the vertical line test and the horizontal line test.

The given graph doesn’t pass the horizontal line test as the value of the function is 2 at two different values.

The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.Option (d) is correct.

Option (a) is not correct.

Option (b) is not correct.

Option (c) is not correct.

Option (d) is correct.

Kindly refer to the image attached.

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Conic section

Keywords: one-to-one, onto, graph representation, paired, y-value, x-values, origin, multiple, single,translation, equation, parabola, shift left, shift right, horizontal, vertical, before translation, after translation.