Use the following graph of the function f(x) = −3x4 − x3 + 3x2 + x + 3 to answer this question: graph of negative 3 x to the fourth, minus x cubed, plus 3 x squared, plus x plus 3 what is the average rate of change from x = 0 to x = 1?

The average rate of change from x=0 to x=1 for f(x) is 0.

Step-by-step explanation:

We are given the function .

Now, the rate average rate of change of a function from to is given by .

As, we need the rate of change from x = 0 to x = 1.

So, we will find the values of f(0) and f(1).

i.e. i.e. f(0)  = 3

and i.e. i.e. f(1) = 3

Thus, the rate of change from x=0 to x=1 is i.e.   i.e. 0

Hence, the average rate of change from x=0 to x=1 for f(x) is 0.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.