Question

The function fgraphed below is defined by a polynomial expression of degree 4. Use the graph to solve the exercise.

(a) If fis increasing on an interval, then the y-values of the points on the graph ____as the x-values increase. From the graph of fwe see that f is increasing on the intervals ____and ____ .

(b) ) If fis decreasing on an interval, then the y-values of the points on the graph ____as the x-values increase. From the graph of f we see that f is increasing on the intervals ____ and ____ .

Short answer

1. Write $\text{'}a\text{'}$by filling all the gaps given in step 1.
2. Write$\text{'}b\text{'}$ by filling all the gaps in step 1.

Step-by-step solution

Part a. Step 1. Filling all the gap.

(a) Increases $\left(1,2\right)$ and $\left(4,5\right)$.

Part a. Step 2. Concept of increasing function.

The function f is said to be increasing when the value of y continuously increases that is $f\left(y_1\right)<f\left(y_2\right)$.

Where $y_1$and $y_2$is at y–axis such that $y_1<y_2$.

Part a. Step 3. Determining the interval.

The function f is increasing in the interval s$\left(1,2\right)$and $\left(4,5\right)$

Part b. Step 1. Filling all the gap.

(b) Decrease$\left(2,4\right)$ and$\left(5,7\right)$

Part b. Step 2. Concept of decreasing function.

The function f is said to be decreasing when the value of y continuously decreases that is $f\left(y_1\right)>f\left(y_2\right)$.

Where $y_1$and$y_2$is at y–axis such that$y_1<y_2.$

Part b. Step 3. Determining the interval.

The function f is decreasing in the interval $\left(2,4\right)$and $\left(5,7\right)$.