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?

i. f(0)=1

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 GFX, and we're given the statement that G 0 is equal to 1. Below the problem, we're given a graph that has our function G of X plotted on it. And this function 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 next segment is also a linear segment. And it goes from the open point at 0.1 to the open point of 1.0. We also have a singular close point located at 1.1. And the last segment is a linear segment that begins at the open point of 1.0 and ends at the close point of 2.1. We're given two possible choices as our answers. For choice A, we have true, and for choice B, we have false. So we need to determine the validity of the statement that G of 0 is equal to 1 using our graph. So in our case here, X is going to be equal to 0. So if you look at our graph, we see that we have 2 points when X is equal to 0 on our graph. We have an open point at 0.1, and we have a close point at 01. So recall for open points that our function actually approaches this point, but never takes on its value, whereas our function takes on the value of a closed point. So that means to determine the value of G of X when X is equal to 0, we're going to want to use the point of 0 minus 1. So that means that G of 0 is going to be equal to -1, which is in contrast to our given statement that G 0 is equal to 1. So that means that our given statement is actually false. So that is the answer that we are looking for for this problem. And if we 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?

i. f(0)=1

Key Concepts

Function Evaluation

Graph Interpretation

True/False Statements

Watch next