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In $3-11$ , each graph shows a polynomial functions from the set of real numbers to the set of real numbers.a. Find the real roots or zeros of the function from the graph, if they exist.b. What is the range of the function?c. Is the function onto?d. Is the function one-to-one?(GRAPH NOT COPY)

a) $x=0$ and $x=2$b) $[1,+\infty)$c) Ontod) Not one-to-one

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 5

Polynomial Functions

An Introduction to Geometry

Functions

Linear Functions

Polynomials

McMaster University

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

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In $3-11$ , each graph sho…

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The range of the polynomia…

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For each graph of a functi…

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05:06

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04:20

Okay, So for this exercise were given the graph of a function and we are asked to determine ah, what the roots of the function are. Ah, what the range of the function is and whether the function is onto or end or 1 to 1. So the first thing I'm gonna do, I'm going to actually right out of the equation for this graph. This is simply the graph of the function Y equals two X plus two. And if we look at the graph right here, we see very clearly that, uh, X equals negative. One is a root or intercept of this particular function. So the root is the only route is negative one because it's a linear function. And now I need to determine the range of the function, which is all the possible output values it could have. Now, since this is a linear function, it extends from negative infinity to positive infinity in both directions. So the range is all real values, so range all real numbers, and we can go ahead and use algebraic notation. Big fancy are to denote all real numbers. So now we need to determine if the function is onto and a function is on two. If given every output, there is some input that produces that output. So we can clearly see that for any why value that we want Thio find on this line There is some X value that will, when we plug it into our equation generate that Why value So the function is aren't too. Now we need to determine if the function is 1 to 1. A 1 to 1 function is a function where for ever every output there is on Lee one input that produces that output. So we can see that if we wanted to produce an output of positive too. The only input we can give is zero. Because if we plug zero in the ER, no other number is going to generate positive too. Except for zero on this process can be repeated for any potential input of potential output pairs. So the answer is yes. This is a 1 to 1 function. Generally, in fact, no, consistently all linear functions are going to be both one toe

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