Decoding Visually

$\newenvironment {prompt}{}{} \newcommand {\accordion }[0]{} \newcommand {\ungraded }[0]{} \newcommand {\xmDefaultPreamble }[0]{xmPreamble.tex} \newcommand {\xmDefaultPrintstyle }[0]{xmPrintstyle.sty} \newcommand {\todo }[0]{} \newcommand {\oiint }[0]{{\large \bigcirc }\kern -1.56em\iint } \newcommand {\mooculus }[0]{\textsf {\textbf {MOOC}\textnormal {\textsf {ULUS}}}} \newcommand {\sagemath }[0]{\textsf {SageMath}} \newcommand {\surfaceColor }[0]{violet} \newcommand {\surfaceColorTwo }[0]{redyellow} \newcommand {\sliceColor }[0]{greenyellow} \newcommand {\vector }[1]{\left \langle #1\right \rangle } \newcommand {\sectionOutcomes }[0]{}$

dots to pairs

The graph below is the graph of $y = m(x)$. One of the dots has been highlighted. This dot visually encodes a function pair. How do we decipher the pair represented by this dot?

$\blacktriangleright $ desmos graph

This browser does not support embedded elements.

We need the coordinates of this dot. To obtain these, we move perpendicularly from the dot to the axes.

$\blacktriangleright $ desmos graph

This browser does not support embedded elements.

From there we can identify the domain number, $-1$, and its range partner (function value), $-3.52$. We now know that $m(-1)=-3.5$.

According to the graph for $y = m(x)$ above, $m(2) = \answer [tolerance=0.3]{1.8}$

According to the graph for $y = m(x)$ above, $m(0)$ is positivenegative.

According to the graph for $y = m(x)$ above, $m(1.8)$ $<$$>$ $m(3.2)$.

Below is the graph for $k = T(w)$. Use this graph to answer the following questions.

$\blacktriangleright $ desmos graph

This browser does not support embedded elements.

$T(-5) = \answer [tolerance=0.3]{10}$
$T(-1) = \answer [tolerance=0.3]{-6}$
$T(4) = \answer [tolerance=0.3]{-3}$
$T(8) = \answer [tolerance=0.3]{1}$

Below is the graph for $k = T(w)$. Use this graph to answer the following questions.

$\blacktriangleright $ desmos graph

This browser does not support embedded elements.

Which of the expressions below best describes the domain of $T$?
$[-7,8]$ $[-6,6]$ $[-7,-1] \cup [3,8]$ $[-7,-1] \cup (3,8]$
Which of the expressions below best describes the range of $T$?
$[-6,6]$ $(-4, 1]$ $[-6,6] \cup (-4,1]$ $[-6,6] \cup [-4,1]$

Below is the graph for $z = w(t)$.

$\blacktriangleright $ desmos graph

This browser does not support embedded elements.

According to the graph, how many solutions are there to the equation $w(t) = 2$?
$0$ $1$ $2$ $4$
According to the graph, how many solutions are there to the equation $w(t) = 0$?
$0$ $1$ $2$ $4$
According to the graph, how many solutions are there to the equation $w(t) = -3$?
$0$ $1$ $2$ $4$

ooooo-=-=-=-ooOoo-=-=-=-ooooo
more examples can be found by following this link
More Examples of Function Graphs

2025-08-01 22:30:38