Question

which part of a graph shows where the function is decreasing?

where the graph goes up from left to right
where the graph goes down from left to right
where the graph is flat
where the graph crosses the y-axis

Explanation:

Define decreasing functions

Using the Definition of a Function knowledge point, we analyze how a function behaves when it is decreasing. A function is decreasing on an interval if, as the input values \(x\) increase from left to right, the output values \(y\) decrease.

Interpret graphical behavior

Using the Linear Graphs knowledge point, we translate this mathematical definition into visual behavior on a coordinate plane. As we move from left to right along the horizontal axis, a decreasing function's graph must move downward along the vertical axis.

Evaluate the given options

We compare our visual interpretation with the provided multiple-choice options:

• "Where the graph goes up from left to right" describes an increasing function.
• "Where the graph goes down from left to right" matches our definition of a decreasing function.
• "Where the graph is flat" describes a constant function.
• "Where the graph crosses the y-axis" describes the y-intercept.

Answer:

• Where the graph goes up from left to right
• Where the graph goes down from left to right (Correct answer)
• Where the graph is flat
• Where the graph crosses the y-axis