few_shots: 
Example:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

Now, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: fl_problem_001894_pos_0

HS_0
standard_description: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
problem_activity: Problem 1
Given the graph below, over which interval is the average rate of change the greatest? Explain your reasoning.
[IMG]
a. Between
$${f(4)}$$
and
$${f(10)}$$
b.
$${10 \leq x \leq 15}$$
c. Between
$${(0,0)}$$
and
$${(4,11)}$$
d. From
$${x=0}$$
to
$${x=10}$$
Problem 2
The table below defines the relationship
$${y=f(x)}$$
.
Find the average rate of change from
$${f (0)}$$
to
$${f(5)}$$
.
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "width:30%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$x$$"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "0"}, {"_attributes": {"style": "text-align:center"}, "_value": "0"}, {"_attributes": {"style": "text-align:center"}, "_value": "4"}, {"_attributes": {"style": "text-align:center"}, "_value": "5"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$f(x)$$"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "26"}, {"_attributes": {"style": "text-align:center"}, "_value": "17"}, {"_attributes": {"style": "text-align:center"}, "_value": "5"}, {"_attributes": {"style": "text-align:center"}, "_value": "1"}]}]}]}]}
Problem 3
You leave from your house at 12:00 p.m. and arrive to your grandmother’s house at 2:30 p.m. Your grandmother lives 100 miles away from your house.
What was your average speed over the entire trip from your house to your grandmother’s house?


aligns: yes