DuckieDai Exponential Transform Solver Python Program

exponential functions · MIT License

Overview

Describe the graph of y = a*b^(x-h)+k: growth or decay, reflection, stretch, shifts, asymptote, domain, range, y-intercept, and three graph points.

Owner-tested on a TI calculator
Version 1.0.0
3302 bytes
No imports

Download EXPTRAN.py Read the source How to install

Before you run it

TI-84 Plus CE Python · No calculator OS or Python App version has been verified.
TI Connect CE .py transfer to the Python App; the owner's transfer details were not recorded
The function is written in the form y = a*b^(x-h)+k.
Values are shown rounded to four decimal places.
a cannot be 0.

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Learn the maths

How exponential transformations work

The standard form

An exponential function can be written in the form below. The program asks for the four numbers a, b, h, and k, then describes the graph one screen at a time.

y = a*b^(x-h)+k

a: the multiplier. Bigger than 1 (ignoring its sign) stretches the graph vertically; between 0 and 1 shrinks it. A negative a flips the graph over the x-axis.
b: the base. Greater than 1 means growth; between 0 and 1 means decay. It must be positive and cannot be 1.
h: the left or right shift. A positive h moves the graph right; a negative h moves it left.
k: the up or down shift. It also sets the horizontal asymptote, y = k.

Watch the sign of h. The form uses x - h, so 3^(x+2) means h = -2, a shift 2 to the left.

What the program reports

Behavior: growth or decay, whether the graph is flipped over the x-axis, and any vertical stretch or shrink.
Shifts: left or right by h, up or down by k, and the horizontal asymptote y = k.
Domain and range: the domain is always all real numbers. The range is above k when a is positive and below k when a is negative.
Y-intercept: the value of y when x is 0.
Three graph points at x = h - 1, h, and h + 1, which are enough to sketch the curve.

The three points always have the y-values a/b + k, a + k, and a*b + k.

Worked example

y = 2*3^(x-1)-4

Enter a = 2, b = 3, h = 1, k = -4. The program reports:

Base: GROWTH, no x-axis flip, vertical stretch by 2.
Right 1, Down 4, asymptote y = -4.
Domain (-inf, inf) and range (-4, inf).
Y-intercept (0, -3.3333).
Graph points (0, -3.3333), (1, -2), and (2, 2).

Answers are rounded to four decimal places, so -3.3333 stands for -10/3.

Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

"""DuckieDai Exponential Transform Solver for TI-84 Plus CE Python."""

def duckiedai_intro(program_name):
    title = program_name[:16]
    empty = 16 - len(title)
    left = empty // 2
    right = empty - left

    print("+----------------------+")
    print("|   " + " " * left + title + " " * right + "   |")
    print("|                      |")
    print("|       __             |")
    print("|   ___(o )>  quack!   |")
    print("|   \\ <_. )           |")
    print("|    `---'             |")
    print("|     by DuckieDai     |")
    print("| hiddenwordscanner.com|")
    print("+----------------------+")
    print("Loading...")
    input("Press enter ")
    print("\n" * 7)


def pause():
    input("\nPress enter ")
    print("\n" * 7)


def num(prompt):
    while True:
        try:
            return float(input(prompt))
        except:
            print("Enter a number.")


def fmt(n):
    if abs(n) < 0.000001:
        n = 0

    if n == int(n):
        return str(int(n))

    return str(round(n, 4))


def run_solver():
    print("STANDARD FORM")
    print("")
    print("y = a*b^(x-h)+k")
    print("")
    print("a = multiplier")
    print("b = base")
    print("h = left/right")
    print("k = up/down")
    pause()

    while True:
        a = num("a? ")

        if a == 0:
            print("a cannot be 0.")
            continue

        b = num("b? ")

        if b <= 0 or b == 1:
            print("b must be > 0")
            print("and not equal 1.")
            continue

        h = num("h? ")
        k = num("k? ")
        break

    print("\n" * 7)
    print("BEHAVIOR")
    print("")

    if b > 1:
        print("Base: GROWTH")
    else:
        print("Base: DECAY")

    if a < 0:
        print("Reflect over")
        print("x-axis")
    else:
        print("No x-axis flip")

    aa = abs(a)

    if aa > 1:
        print("Vertical stretch")
        print("by " + fmt(aa))
    elif aa < 1:
        print("Vertical shrink")
        print("by " + fmt(aa))
    else:
        print("No stretch")

    pause()

    print("SHIFTS")
    print("")

    if h > 0:
        print("Right " + fmt(h))
    elif h < 0:
        print("Left " + fmt(abs(h)))
    else:
        print("No left/right")

    if k > 0:
        print("Up " + fmt(k))
    elif k < 0:
        print("Down " + fmt(abs(k)))
    else:
        print("No up/down")

    print("")
    print("ASYMPTOTE")
    print("y = " + fmt(k))

    pause()

    print("DOMAIN")
    print("(-inf, inf)")
    print("")
    print("RANGE")

    if a > 0:
        print("(" + fmt(k) + ", inf)")
    else:
        print("(-inf, " + fmt(k) + ")")

    print("")
    yint = a * (b ** (-h)) + k
    print("Y-INTERCEPT")
    print("(0, " + fmt(yint) + ")")

    pause()

    print("GRAPH POINTS")
    print("")

    x1 = h - 1
    y1 = a * (b ** -1) + k

    x2 = h
    y2 = a + k

    x3 = h + 1
    y3 = a * b + k

    print("(" + fmt(x1) + ", " + fmt(y1) + ")")
    print("(" + fmt(x2) + ", " + fmt(y2) + ")")
    print("(" + fmt(x3) + ", " + fmt(y3) + ")")

    print("")
    print("HA: y = " + fmt(k))


duckiedai_intro("Exp Transform")

while True:
    run_solver()

    print("")
    again = input("Again? y/n: ")

    if again.lower() != "y":
        break

    print("\n" * 7)

print("\nDuckieDai says:")
print("done!")

"""DuckieDai Exponential Transform Solver for TI-84 Plus CE Python."""
def duckiedai_intro(program_name):
title = program_name[:16]
empty = 16 - len(title)
left = empty // 2
right = empty - left
print("+----------------------+")
print("| " + " " * left + title + " " * right + " |")
print("| |")
print("| __ |")
print("| ___(o )> quack! |")
print("| \\ <_. ) |")
print("| `---' |")
print("| by DuckieDai |")
print("| hiddenwordscanner.com|")
print("+----------------------+")
print("Loading...")
input("Press enter ")
print("\n" * 7)
def pause():
input("\nPress enter ")
print("\n" * 7)
def num(prompt):
while True:
try:
return float(input(prompt))
except:
print("Enter a number.")
def fmt(n):
if abs(n) < 0.000001:
n = 0
if n == int(n):
return str(int(n))
return str(round(n, 4))
def run_solver():
print("STANDARD FORM")
print("")
print("y = a*b^(x-h)+k")
print("")
print("a = multiplier")
print("b = base")
print("h = left/right")
print("k = up/down")
pause()
while True:
a = num("a? ")
if a == 0:
print("a cannot be 0.")
continue
b = num("b? ")
if b <= 0 or b == 1:
print("b must be > 0")
print("and not equal 1.")
continue
h = num("h? ")
k = num("k? ")
break
print("\n" * 7)
print("BEHAVIOR")
print("")
if b > 1:
print("Base: GROWTH")
else:
print("Base: DECAY")
if a < 0:
print("Reflect over")
print("x-axis")
else:
print("No x-axis flip")
aa = abs(a)
if aa > 1:
print("Vertical stretch")
print("by " + fmt(aa))
elif aa < 1:
print("Vertical shrink")
print("by " + fmt(aa))
else:
print("No stretch")
pause()
print("SHIFTS")
print("")
if h > 0:
print("Right " + fmt(h))
elif h < 0:
print("Left " + fmt(abs(h)))
else:
print("No left/right")
if k > 0:
print("Up " + fmt(k))
elif k < 0:
print("Down " + fmt(abs(k)))
else:
print("No up/down")
print("")
print("ASYMPTOTE")
print("y = " + fmt(k))
pause()
print("DOMAIN")
print("(-inf, inf)")
print("")
print("RANGE")
if a > 0:
print("(" + fmt(k) + ", inf)")
else:
print("(-inf, " + fmt(k) + ")")
print("")
yint = a * (b ** (-h)) + k
print("Y-INTERCEPT")
print("(0, " + fmt(yint) + ")")
pause()
print("GRAPH POINTS")
print("")
x1 = h - 1
y1 = a * (b ** -1) + k
x2 = h
y2 = a + k
x3 = h + 1
y3 = a * b + k
print("(" + fmt(x1) + ", " + fmt(y1) + ")")
print("(" + fmt(x2) + ", " + fmt(y2) + ")")
print("(" + fmt(x3) + ", " + fmt(y3) + ")")
print("")
print("HA: y = " + fmt(k))
duckiedai_intro("Exp Transform")
while True:
run_solver()
print("")
again = input("Again? y/n: ")
if again.lower() != "y":
break
print("\n" * 7)
print("\nDuckieDai says:")
print("done!")

Filename: EXPTRAN.py
Size: 3302 bytes
SHA-256: e371a928d3e55565624535284d3acb2d3bcb83dc429b709f3256b2882f20bd19

Usage

Inputs

Multiplier a (not 0)
Base b (positive and not 1)
Horizontal shift h
Vertical shift k

Outputs

Growth or decay, x-axis reflection, and vertical stretch or shrink
Left/right and up/down shifts with the horizontal asymptote y = k
Domain, range, and y-intercept
Three graph points at x = h-1, h, and h+1

Units: Function parameters; no physical units.

Assumptions and limitations

Assumptions

The function is written in the form y = a*b^(x-h)+k.
Values are shown rounded to four decimal places.

Constraints

a cannot be 0.
b must be greater than 0 and cannot equal 1.

Known failures

A very large shift or base makes the y-intercept or a graph point too large for the calculator and stops the program with an error.
An invalid a or b restarts entry from a.

Compatibility and review

Review status: Owner-tested on a TI calculator
Tested on: Owner reports personally using this program on a TI-84 Plus CE Python calculator for coursework; the test date, OS version, and Python App version were not recorded
What happened: Owner reported pass on the calculator before the website line was added to the opening screen and the line endings were normalised. The steps after the opening screen are unchanged; this exact file has not yet been rerun on a calculator.
Dependencies: No imports
Suggested calculator name: EXPTRAN — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Transfer and launch

Confirm that your calculator is the Python-capable model named above. This release has no verified calculator OS or Python App version; treat transfer and execution as unverified until independently tested.
Download the .py source above and verify its SHA-256 digest if your computer provides that option.
Use TI Connect CE to send the Python file to a compatible calculator. EXPTRAN is a suggested name; you may choose another valid, unique calculator name.
Open the Python App, select the program, and check sample inputs before relying on other results.

Read the complete installation, launch, troubleshooting, and removal guide.

Availability does not mean a teacher, school, or exam permits this program. Follow the applicable rules.

Version history

1.0.0 — current version, published 2026-10-05. Download this reviewed version

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Related guide

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