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


i. f(0)=1

Verified step by step guidance

1. Examine the graph of the function y = f(x) at the point where x = 0. This involves identifying the y-coordinate of the point on the graph that corresponds to x = 0.
2. Determine the value of f(0) by observing the y-coordinate of the point on the graph where x = 0. This value is the output of the function when the input is 0.
3. Compare the observed value of f(0) with the given statement f(0) = 1. Check if the y-coordinate at x = 0 matches the value 1.
4. If the y-coordinate at x = 0 is equal to 1, then the statement f(0) = 1 is true. Otherwise, the statement is false.
5. Conclude whether the statement is true or false based on the comparison made in the previous step. This involves confirming the accuracy of the statement by referencing the graph.

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. For example, if f(x) is a function, then f(0) means we are looking for the value of the function when x equals 0. Understanding how to read and interpret function values from a graph is crucial for answering questions about specific points on the graph.

Graph Interpretation

Graph interpretation is the ability to analyze and extract information from a visual representation of a function. This includes identifying key points, such as intercepts and local maxima or minima, as well as understanding the overall shape and behavior of the graph. In this context, it is essential to determine the value of f(0) by locating the point where the graph intersects the y-axis.

True/False Statements

True/false statements require critical thinking to assess the validity of claims based on given information. In calculus, this often involves verifying whether a specific condition holds true for a function, such as checking if f(0) equals a certain value. This process typically involves both analytical skills and visual confirmation from the graph.