Given the following function:
Is the function increasing or decreasing?
We have hundreds of course questions with personalized recommendations + Account 100% premium
Given the following function:
Is the function increasing or decreasing?
To determine if the function is increasing or decreasing, we need to consider its slope.
The function is a linear function of the form , where:
The slope is the rate of change of the function. For linear functions:
In this case, the slope is negative (). This indicates that as increases, decreases, meaning the function is decreasing.
Therefore, the function is decreasing.
Decreasing
Is the function in the graph decreasing?
The slope tells us the rate of change. When the slope is negative, like -2, it means for every 1 unit increase in x, y decreases by 2 units. So as we move right, we go down!
Look at the coefficient of x (the slope). If it's positive, the function increases. If it's negative, the function decreases. For , the coefficient is -2, so it's decreasing.
The -2 is the slope of the line. It means for every 1 step right (positive x direction), you take 2 steps down (negative y direction). That's why the line slopes downward!
Absolutely! Try x = 0: y = -2(0) = 0. Try x = 1: y = -2(1) = -2. Try x = 2: y = -2(2) = -4. Notice how as x gets bigger, y gets smaller? That's decreasing!
Yes! These are the same equation written differently. Both represent the same decreasing line with slope -2. You can rearrange one form to get the other.
Get unlimited access to all 18 Functions questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime