FN1 Check It

[tdegeorge]

Reviewer: @AbbyANoble

UPDATED

Task 1: Which of the following relations are functions? Explain your reasoning. (Vary on each instance whether the ordered pairs, table, and mapping are or are not functions).

• Set of ordered pairs
• A table
• A mapping notation

Task 2: Determine which of the two equations represents a function. Explain your reasoning.

Examples (these are just a couple to consider - choose equations where one is a function and one is not). Can vary coefficients and exponents (as long as one is a function):

• x^2+y=0 versus x+y^2=0
• x^2+y^3=0 versus x^3+y^2=0

Task 3: Determine whether each graph is a function. Explain your reasoning.

Choose three graphs to give students (vary them):

• graph of an ellipse
• graph of a parabola
• graph of a set of points
• non-function "sideways" parabola
• set of points that is a function
• line (including horizontal and vertical ones too)
• cubic
• circle
• hyperbola
• piecewise, both functions and non-functions

[AbbyANoble]

Task 1 -

I think it should vary on each instance whether the ordered pairs, table, and mapping are or are not functions rather than having each one set as a function or not.

[AbbyANoble]

Task 2 - I like this one! Would we want to say that in the pair there is one function and one non-function and for them to explain how they know the difference?

[AbbyANoble]

Task 3 - I think rather than saying to use the vertical line test, I'd say to determine whether or not each is a function, then explain your answer. Then they have more leeway to appeal to vertical line test or give points that make it not a function.

And I think there would need to be more options to choose three from. Other options could be:

• non-function "sideways" parabola
• set of points that is a function
• line (including horizontal and vertical ones too)
• cubic
• circle
• hyperbola
• piecewise, both functions and non-functions

[siwelwerd]

Testing out sageplots for mapping notation before implementing this... what do we think of this? @AbbyANoble @tdegeorge @kathypinzon

p=ellipse((-2,0),1,2,fill=True,alpha=0.3)
p+=ellipse((2,0),1,2,fill=True,alpha=0.3)
p+=arrow( (-2,1.5), (2,-1.5))
p+=arrow( (-2,1.5), (2,1.5))
p+=arrow( (-2,0), (2,-1.5))
p+=arrow( (-2,-1.5), (2,0))
p+=text("$2$", (-2,1.5),fontsize=20,horizontal_alignment="right",color="black")
p+=text("$3$", (-2,0),fontsize=20,horizontal_alignment="right",color="black")
p+=text("$4$", (-2,-1.5),fontsize=20,horizontal_alignment="right",color="black")
p+=text("$5$", (2,1.5),fontsize=20,horizontal_alignment="left",color="black")
p+=text("$6$", (2,0),fontsize=20,horizontal_alignment="left",color="black")
p+=text("$7$", (2,-1.5),fontsize=20,horizontal_alignment="left",color="black")
p.axes(False)
show(p)

[siwelwerd]

Thought for task 2: if $f$ is a bijection and $g$ is not injective, then $f(y)=g(x)$ is a function but $f(x)=g(y)$ is not. This generalizes $y^3=x^2$ vs. $x^3=y^2$.

[siwelwerd]

I think this is a great problem, but it's a lot to implement! Got 2 of the 3 tasks done.