Give the function:
f (x)= -2x+4, 0 (greater or less than) x (greater or equal to) 8
-5x+11, x (less than or equal to) 8
(I have soo much trouble with these!)
^^contiued question
Is the function increasing or decreasing over the interval [2,7]?
f(x) =
{ -2x+4 for x≤0 or x≥8
{ -5x+11 for 0 < x < 8
so, on the interval [2,7] the slope is -5, so decreasing
You should always graph functions if you are not sure.
No worries, I'm here to help! This function is defined piecewise, meaning it has different formulas for different intervals of x. Let's break it down step by step.
1. The first condition states that if x is greater than or equal to 8, the function is defined as -2x + 4.
2. The second condition states that if x is less than or equal to 8, the function is defined as -5x + 11.
To evaluate the function for a specific value of x, follow these steps:
1. Determine the interval in which the given x value falls. In this case, we have two intervals: x greater than or equal to 8, and x less than or equal to 8.
2. If the x value falls within the first interval (x greater than or equal to 8), substitute the x value into the formula -2x + 4 and simplify to find the corresponding y value.
3. If the x value falls within the second interval (x less than or equal to 8), substitute the x value into the formula -5x + 11 and simplify to find the corresponding y value.
Let's work through an example:
If we want to find the value of f(x) when x = 6, we follow these steps:
1. Since x = 6 falls within the second interval (x less than or equal to 8), we will use the formula -5x + 11.
2. Substitute x = 6 into the formula: f(x) = -5(6) + 11 = -30 + 11 = -19.
Therefore, when x = 6, f(x) = -19.
I hope this explanation helps you understand how to evaluate piecewise functions! If you have any more questions, feel free to ask.