$\bold{%v}$

$\bold{%v}$

$\bold{%v}$

\textsf{Drag the point and use \
the slider to explore shifts\and 
stretching of functions.}

$\text{SHOW PARENT FUNCTION}$

\textsf{Exponential functions are defined}\
\textsf{for }b>0 \textsf{ and }b\ne 1.

\text{Base}

x

y

a = 1 (slider from -5 to 5, step 0.1)
b = 2 (slider from 0 to 5, step 0.1)
PP1: (-11.29, -11.29)
PP2 = Mirror(PP1, yAxis)
PP3 = Mirror(PP2, xAxis)
bigGrid = Sequence(Sequence[(j, k), j, -10, 10, 1], k, -10, 10, 1)
A = Point(bigGrid)
P = Point(bigGrid)
k: y(P)
h: x(P)
B = (2, 0)
C = (0, 4)
T = (-5, -5)
J = (-2, 0)
PP4 = Mirror(PP3, yAxis)
peep, p1, p1', p1'', p1''' = Polygon(PP1, PP2, PP3, PP4)
allA = Shuffle(Sequence[t, t, -18, 18])
countQuestion: 1
valA = Element(allA, Mod[countQuestion, Length[allA]] + 1)
speed: 1
textFun: "f(x)=" + (LaTeX[If[a ≟ 0, "0", a ≟ 1, (("(\textcolor{#6557D2}" * b) * ")^x"), a ≟ -1, (("\textcolor{#DA2570}{ - }(\textcolor{#6557D2}{" * b) * "})^x"), (((("\textcolor{#DA2570}{" * a) * "}(\textcolor{#6557D2}{") * b) * "})^x")]]) + ""
parent(x) = b^(x)
D: (0, 1)
showParent = false
textBase: "\textcolor{#DA2570}{" + (LaTeX[If[a > 1, "a>1", a < -1, "a<-1", 0 < a < 1, "0<a<1", a ≟ -1, "a=-1", "-1<a<0"]]) + "}\\\\" + (LaTeX[If[a > 1 ∨ a < -1, "\textsf{vertical stretch}", a ≟ -1, "\textsf{reflection about the }x \textsf{-axis}", "\textsf{vertical compression}"]]) + ""
ao: y = y(A) - 1
onboarding = true
pulsingSpeed: 8
pulsing = 0.9 (slider from 0 to 1, step 0.1)
labelStretch = VerticalText("\textsf{Stretch}")
yTicks = Sequence((0, k), k, -10, 10, 1)
xTicks = Sequence((k, 0), k, -10, 10, 1)
fakeX = Segment((x(PP1) + 0.05, 0), ((-x(PP1)) - 0.05, 0))
fakeY = Segment((0, y(PP1) + 0.05), (0, (-y(PP1)) - 0.05))
par(x) = (a * (x - h)^(2)) + k
av(x) = (a * abs(x - h)) + k
esp(x) = (a * b^(x - h)) + k
pulsingObject = circlePixels(P, 7 + (7 * pulsing), Corner[1], Corner[3], Corner[5])
fake(x) = (a * x^(2)) + k
textAllFun: "\textsf{\textcolor{#5145A8}{\underline{Exponential}}}\\
\textcolor{#5145A8}{f(x)=" + (LaTeX[esp]) + "}\\\\\\
\textsf{\textcolor{#0F8538}{\underline{Quadratic}}}\\
\textcolor{#0F8538}{g(x)=" + (LaTeX[If[x(P) ≠ 0, par, fake]]) + "}\\\\\\
\textsf{\textcolor{#C75000}{\underline{Absolute value}}}\\
\textcolor{#C75000}{h(x)=" + (LaTeX[av]) + "}"
tabOrder: {textQuestion, textAllFun, P, textSli, b, labelStretch, a, textBase, textNotDef}

Tool: circlePixels
circlePixels(A,pixelRadius,Corner1,Corner3,Corner5
Input: A, pixelRadius, Corner1, Corner3, Corner5
Output: newCircle

pointRadius: (pixelRadius / x(Corner5) * (x(Corner3) - x(Corner1)))
newCircle = Circle(A, pointRadius)