Question

knowledge
functions, domain, range

1. complete the table below.

10

image	functions or not a function	domain	range
image of a function mapping	function
image of a non - function circle graph	not a function
image of a non - function graph	not a function

k/u 1/14
app 1/14

Explanation:

Step1: Recall domain and range definitions

Domain is the set of all input values (x - values), range is the set of all output values (y - values).

Step2: Analyze the second example (function)

The domain is the set of input values from the left - hand set in the mapping diagram. Here, the domain is $\{0,1,2,3\}$. The range is the set of output values from the right - hand set in the mapping diagram, so the range is $\{2,4,9\}$.

Step3: Analyze the third example (not a function, circle)

For a circle centered at the origin with equation $x^{2}+y^{2}=r^{2}$, solving for $y$ gives $y=\pm\sqrt{r^{2}-x^{2}}$. The domain is the set of all possible $x$ values. For a standard circle, the domain is $(-r,r)$. Assuming a unit circle ($r = 1$), the domain is $(- 1,1)$. The range is also $(-1,1)$ since $y$ values range from $-1$ to $1$.

Step4: Analyze the fourth example (not a function, set of points)

The domain is the set of all $x$ - coordinates of the points. Looking at the points, the domain is $\{-2,-1,0,1,2\}$. The range is the set of all $y$ - coordinates of the points, which is $\{-2,-1,0,1,2\}$.

Answer:

Image	Functions or Not a Function	Domain	Range
Third example (circle)	Not a Function	$(-1,1)$	$(-1,1)$
Fourth example (set of points)	Not a Function	$\{-2,-1,0,1,2\}$	$\{-2,-1,0,1,2\}$