Determine whether the function is increasing, decreasing, or constant. For each function, check your answers using a graph or a table:
Each number is multiplied by 0.5.
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Determine whether the function is increasing, decreasing, or constant. For each function, check your answers using a graph or a table:
Each number is multiplied by 0.5.
The function is:
Let's start with x equal to 0:
Now let's assume x is equal to 1:
Now let's assume x is equal to 2:
Let's record all the data in a table:
Note that the function is always increasing.
Growing
Is the function in the graph decreasing?
Great question! You're thinking about one multiplication, but function behavior compares different inputs. When x grows from 1 to 2, f(x) grows from 0.5 to 1. The function is increasing even though each output is half its input.
Look at the coefficient of x (the slope)! If it's positive like 0.5, the function increases. If negative like -0.5, it decreases. If zero, it's constant.
No! For linear functions, testing just 2-3 values is enough. If f(1) < f(2) < f(3), the function is increasing everywhere. Linear functions have constant behavior.
Both methods show the same thing! In a table, look for f(x) values getting larger. On a graph, look for a line going upward from left to right. Use whichever feels easier!
Not for linear functions! They have constant slope, so they're either always increasing, always decreasing, or always constant. Only curved functions can increase in some places and decrease in others.
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