Which of the following statements about the function y=f(x) gr...

Question

Which of the following statements about the function y=f(x) graphed here are true, and which are false?

h. f(0)=0

Accepted Answer

Hi, everyone. Let's take a look at this practice problem. This problem says determine the validity of the following statement based on the given graph of Y is equal to G of X, and we're given the statement that G1 is equal to 0. Below the problem we're given a graph that has our function G of X plotted on it. And G of X is a piecewise function. The first piece is a linear piece, and it goes from the close point at -1.0 to the close point of 0.1. The second piece is a linear piece, and it goes from the open point of 0.1 to the open point of 1.0. We have a singular close point located at 1.1. And the last segment is a linear segment, and it goes from the open point of 1.0 to the close point of 2.1. We're also given two possible choices as our answers. For choice A we have true, and for choice B, we have false. So for this problem, we need to determine the validity of our statement that G of 1 is equal to 0 using our graph. And so, in this case, we're going to be looking at the case when X is equal to 1. And so on a graph, we see that when X is equal to 1, we actually have two points. We have an open point at 1.0 and a close point at 1.1. Now we call for open points that our function actually approaches this point. However, it never takes on the value at that point. But for a close point, that is going to be the value that our function takes at that point. So determine the value of G of X when X is equal to 1, we're going to want to use the close point located at 11. So that means that G of 1. is equal to -1. And this is in direct contrast to the statement that we're given that G of 1 is equal to 0. So that means that our given statement is actually false. So that is the the answer that we were looking for for this problem. And so now if we can compare our answer to our answer choices, we see that the correct answer choice corresponds to answer choice B. So I hope that this explanation has been useful and I'll see you in the next video.

Which of the following statements about the function y=f(x) graphed here are true, and which are false?

h. f(0)=0

Key Concepts

Function Evaluation

Graph Interpretation

True/False Statements

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