Exploring Functions and Inequalities

What does f(x) > 0 indicate about a graph's position?

• The graph intersects the x-axis

• The graph is at the origin

• The graph is below the x-axis

• The graph is above the x-axis

How is the x-axis represented in the context of y?

• y = 1

• y = x

• y = 0

• y = -1

What symbol is used in interval notation to represent an open endpoint?

• A square

• A curly brace

• A parenthesis

• A bracket

For a function f(x) < 0, where is the graph positioned?

• Above the x-axis

• Below the x-axis

• Parallel to the y-axis

• On the x-axis

What does an x-intercept represent?

• The lowest point of the graph

• The highest point of the graph

• Where the graph crosses the x-axis

• Where the graph touches the y-axis

In interval notation, what does a bracket signify?

• An open interval

• An infinite limit

• A closed interval

• A non-inclusive value

How are x-values where f(x) is greater than or equal to zero represented?

• With no symbols at all

• With parentheses on both ends

• With a mix of brackets and parentheses

• With brackets on both ends

What is the significance of the green line in the examples?

• It represents the maximum value of f(x)

• It separates different intervals of x

• It indicates where f(x) = 0

• It shows the boundary for negative values of f(x)

What does it mean if a graph has multiple sections above the green line?

• The function is undefined

• The function has multiple roots

• The function is constant

• The function has multiple intervals where it is greater than zero

Why might a point on a graph have a parenthesis in interval notation?

• It's the highest value of the function

• It's a closed endpoint

• It's an error in the graph

• It's an open endpoint