few_shots: 
Example 1:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

Example 2:
Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Concept/skill: 
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Answer: 
No. This task does not involve an equation in two variables. There is only one variable, x.

Example 3:
Problem/activity:
Task
Suppose $A$ is an angle with vertex $P$, as pictured below:
[IMG]
Draw a circle with center $P$ and with  radius $r \gt 0$.  Explain why the circle
meets each ray of angle $A$ in a single point.  Label these points $Q$ and $R$ respectively.
Draw circles with centers $Q$ and $R$ respectively and radius $r$.  These circles meet at $P$ and a second point to be labelled $B$.
Show that ray $\overrightarrow{PB}$  bisects angle $P$.


Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

Answer: 
No. This task does not involve drawing lines that are tangent to circles. The only line that may be drawn is the ray between points P and B.

Now, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001894_neg_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Find inverse functions.
problem_activity: Problem 1
Below is the parent function of a quadratic function:
[IMG]
Given the equation in vertex form and the corresponding graph, identify the transformations to each function.
| **           Equation          ** |                             **           Graph          **                              | **           Transformation(s)          ** |
|-----------------------------------|-----------------------------------------------------------------------------------------|--------------------------------------------|
|       $${g(x)=(x+1)^2+3}$$        | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap1b.png |                                            |
|       $${r(x)=-2(x-1)^2}$$        | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap1c.png |                                            |
|        $${t(x)=(2x-1)^2}$$        | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap1d.png |                                            |
Problem 2
A quadratic equation is
decreasing over the interval
$${-\infty < x < 3}$$
increasing over the interval
$${3 < x < \infty}$$
and has a rate of change of zero at
$${x=3}$$
.
Describe how each of the three graphs below fit this description.
| .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap2a.png | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap2b.png | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap2c.png |
|-----------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------|


aligns: no