In which domain does the function increase? Green line: $$ x=-0.8 $$ –2 –2 –2 2 2 2 2 2 2 0 0 0

It does not have an increasing domain.

Increasing and Decreasing Functions Practice Problems

Understanding Decreasing function

Complete explanation with examples

Decreasing function

What is a Decreasing Function?

A decreasing function is a type of relationship where, as you move to the right on the graph (increasing the xxx-value), the $y$ -value gets smaller. It’s like going downhill—the farther you go (the more you increase $x$ ), the lower your height (the $y$ -value) becomes.

We will say that a function is decreasing when, as the value of the independent variable $X$ increases, the value of the function $Y$ decreases.

How to Spot a Decreasing Function:

On a Graph: The line or curve goes downward as you move from left to right.
In Numbers: For any two $x$ -values, if the second number is larger than the first $x_2 > x_1$, then the second $y$ -value will be smaller than the first $f(x_2) < f(x_1)$ .

Real-Life Example:

Think about eating a stack of cookies. Every time you eat one, the number of cookies left in the stack gets smaller. That’s a decreasing function—your $y$ -value (cookies left) decreases as your $x$ -value (number of cookies eaten) increases.

Fun Fact:

If the line or curve always goes down without stopping, it's called strictly decreasing. If it flattens for a bit before going down again, it’s just decreasing.

Let's see an example of strictly decreasing linear function on a graph:

Detailed explanation

Practice Decreasing function

Test your knowledge with 17 quizzes

In which interval does the function decrease?

Red line: $$ x=0.65 $$

Examples with solutions for Decreasing function

Step-by-step solutions included

Exercise #1

In what domain does the function increase?

Step-by-Step Solution

Let's remember that the function increases if the $x$ values and $y$ values increase simultaneously.

On the other hand, the function decreases if the $x$ values increase while the $y$ values decrease simultaneously.

In the given graph, we can see that the function increases in the domain where $x > 0$ ; in other words, where the $y$ values are increasing.

Answer:

$x > 0$

Video Solution

Exercise #2

Determine in which domain the function is negative?

Step-by-Step Solution

Remember that a function is increasing if both X values and Y values are increasing simultaneously.

A function is decreasing if X values are increasing while Y values are decreasing simultaneously.

In the graph, we can observe that in the domain $x > 1$ the function is decreasing, meaning the Y values are decreasing.

Answer:

$x > 1$

Video Solution

Exercise #3

In what domain is the function increasing?

Step-by-Step Solution

Let's first remember that a function is increasing if both the X and Y values are increasing simultaneously.

Conversely, a function is decreasing if the X values are increasing while the Y values are decreasing simultaneously.

In the graph shown, we can see that the function is increasing in every domain and therefore the function is increasing for all values of X.

Answer:

All values of $x$

Video Solution

Exercise #4

In what domain does the function increase?

Step-by-Step Solution

Let's remember that the function increases if the X values and Y values increase simultaneously.

On the other hand, the function decreases if the X values increase and the Y values decrease simultaneously.

In the given graph, we notice that the function increases in the domain where $x < 0$ , meaning the Y values are increasing.

Answer:

$x<0$

Video Solution

Exercise #5

In what interval is the function increasing?

Purple line: $x=0.6$

Step-by-Step Solution

Let's remember that a function is described as increasing if both X values and Y values are increasing simultaneously.

A function is decreasing if X values are increasing while Y values are decreasing simultaneously.

In the graph, we can see that in the domain $x < 0.6$ the function is increasing, meaning the Y values are increasing.

Answer:

$x<0.6$

Video Solution

Frequently Asked Questions

Everything you need to know about Decreasing function

How do you find the decreasing interval of a quadratic function?

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For a quadratic function f(x) = ax² + bx + c, first find the vertex x-coordinate using x = -b/(2a). If a > 0 (parabola opens up), the function decreases for x < vertex x-value. If a < 0 (parabola opens down), the function decreases for x > vertex x-value.

What makes a function decreasing vs strictly decreasing?

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A function is decreasing if f(x₂) ≤ f(x₁) whenever x₂ > x₁. A function is strictly decreasing if f(x₂) < f(x₁) whenever x₂ > x₁. Strictly decreasing means the function never stays flat - it always goes down as you move right.

How can you tell if a function is decreasing from its graph?

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Look at the graph from left to right. If the line or curve goes downward (like going downhill), the function is decreasing in that interval. The y-values get smaller as x-values increase.

What's the difference between where a function is decreasing and where it's negative?

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A function is decreasing when its values get smaller as x increases (slope behavior). A function is negative when its y-values are below the x-axis (sign of output). These are completely different concepts - a function can be decreasing but positive, or increasing but negative.

How do you find where a quadratic function changes from increasing to decreasing?

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The turning point occurs at the vertex. For f(x) = ax² + bx + c, calculate x = -b/(2a) to find the vertex x-coordinate. This is where the function switches from increasing to decreasing (or vice versa).

Can a linear function be both increasing and decreasing?

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No, a non-horizontal linear function is either always increasing or always decreasing throughout its entire domain. Only horizontal lines (constant functions) are neither increasing nor decreasing.

What does it mean when a function has intervals of increase and decrease?

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This means the function changes behavior at different x-values. For example, a parabola might decrease until it reaches its vertex, then increase afterward. The function has different behaviors in different intervals of its domain.

How do you write interval notation for decreasing functions?

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Use parentheses for open intervals and brackets for closed intervals. For example, if a function decreases for x < -1, write (-∞, -1). If it decreases for x ≤ 2, write (-∞, 2]. Always use parentheses with infinity symbols.

Continue Your Math Journey

Master Decreasing function first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

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Increasing and Decreasing Functions Practice Problems

Understanding Decreasing function

Decreasing function

What is a Decreasing Function?

How to Spot a Decreasing Function:

Real-Life Example:

Fun Fact:

Practice Decreasing function

Examples with solutions for Decreasing function

Frequently Asked Questions

How do you find the decreasing interval of a quadratic function?

What makes a function decreasing vs strictly decreasing?

How can you tell if a function is decreasing from its graph?

What's the difference between where a function is decreasing and where it's negative?

How do you find where a quadratic function changes from increasing to decreasing?

Can a linear function be both increasing and decreasing?

What does it mean when a function has intervals of increase and decrease?

How do you write interval notation for decreasing functions?

More Decreasing function Questions

Increasing and Decreasing Intervals of a Function

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Suggested Topics to Practice in Advance

Topics Learned in Later Sections

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