Exploring Functions and Relations in Algebra 2

The video tutorial introduces Algebra 2 by discussing functions, their definitions, and how to evaluate them from equations and graphs. It compares functions and relations, explaining that a function has only one output for each input. The video includes a game to identify functions from tables and demonstrates the vertical line test for graphs. Function notation is explained with examples, and the video concludes with evaluating functions from graphs.

Why is Table 2 not a valid function?

• It has more than one input for some outputs.

• It has more than one output for some inputs.

• It has the same output for all inputs.

• It has no outputs.

What is the key difference between a relation and a function?

• A relation has no inputs.

• A function has only one output for each input.

• A relation has only one output for each input.

• A function has multiple outputs for each input.

In the 'Function or Nah' game, why is the second table not a function?

• It has no output values.

• It has no input values.

• It has the same output value with different inputs.

• It has the same input value with different outputs.

What does the vertical line test help determine?

• If a graph has multiple outputs.

• If a graph has multiple inputs.

• If a graph represents a relation.

• If a graph represents a function.

What happens if a vertical line passes through more than one point on a graph?

• The graph has no inputs.

• The graph is a function.

• The graph has no outputs.

• The graph is not a function.

In function notation, what does f(x) represent?

• The input of the function for output x.

• The sum of the function.

• The difference of the function.

• The output of the function for input x.

How do you evaluate f(3) for the function f(x) = 2x^2 + x - 1?

• Substitute 0 for x and solve.

• Substitute 3 for x and solve.

• Substitute 2 for x and solve.

• Substitute 1 for x and solve.

What is the value of f(2) for the function f(x) = 7 - 2x?

• 3

• 9

• 5

• 7

How do you find the output value from a graph for a given input value?

• Locate the input on the x-axis and find the corresponding z-value.

• Locate the input on the y-axis and find the corresponding x-value.

• Locate the input on the y-axis and find the corresponding z-value.

• Locate the input on the x-axis and find the corresponding y-value.

What is the output value for the input x = 2 on the given graph?

• 8

• 6

• 4

• 2