DuckieDai Exp and Log Plot Points Python Program

exponential functions · MIT License

Overview

Give five points to plot for a transformed exponential or logarithmic function, with its asymptote, domain, and range.

Owner-tested on a TI calculator
Version 1.0.0
1857 bytes
Uses math

Download PLOT.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 in the form shown on the menu, with the shift inside written as x-h.
Points come from the parent graph's exponents -2 to 2, so they are easy to plot.
The base must be greater than 0 and not 1; inf and nan are asked for again.

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Learn the math

How to graph transformed exponential and log functions

The idea

Every exponential graph y = b^x passes through a few easy points: (0, 1), (1, b), and (-1, 1/b). A log graph y = log_b(x) is the same curve reflected over the line y = x, so its easy points are (1, 0), (b, 1), and (1/b, -1).

A transformed function moves and stretches those points. h shifts the graph left or right, k shifts it up or down, a stretches it and flips it when negative, and a minus sign inside reflects it across a vertical line. Plot the moved points, draw the asymptote, and the graph follows.

The formula

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

y = a*log_b(x-h) + k

exponential asymptote: y = k; log asymptote: x = h

a: the vertical stretch, flipping the graph when it is negative
b: the base, greater than 0 and not 1
h, k: the horizontal and vertical shifts
asymptote: the line the graph gets closer to but never reaches

Using the program

Choose 1 for an exponential function or 2 for a logarithmic one.
Enter a, the base b, h, and k. Numbers can be fractions such as 1/2, sqrt( ), or e.
Answer 2 to Flip x inside? when the function has a minus sign in front of x - h, as in b^-(x-h).
The program shows five points to plot, then the asymptote, the domain, and the range.

Worked example

Graph y = 2^(x-1) + 3. Choose 1 and enter a = 1, b = 2, h = 1, k = 3, and 1 for no flip.

the points (t, 2^t) of y = 2^x move to (t + 1, 2^t + 3)

The program shows (-1, 13/4), (0, 7/2), (1, 4), (2, 5), and (3, 7), then ASYMPTOTE: y = 3, DOMAIN: (-inf, inf), and RANGE: (3, inf).

Graph y = log_2(x). Choose 2 and enter a = 1, b = 2, h = 0, k = 0, and no flip. The program shows (1/4, -2), (1/2, -1), (1, 0), (2, 1), and (4, 2), with ASYMPTOTE: x = 0 and DOMAIN: (0, inf).

Tips and common mistakes

Shift the asymptote along with the graph: y = 2^(x-1) + 3 levels off at y = 3, not y = 0.
The domain of a log graph starts at its asymptote, so log_2(x - h) needs x greater than h, or less than h when x is flipped.
A base between 0 and 1, such as 1/2, makes an exponential graph fall from left to right.
Plot all five points before drawing; the points far from the asymptote show the shape best.

Where this comes up

Graphing transformed exponential and logarithmic functions is part of the exponential functions unit of algebra 2, precalculus, and college algebra.

Exact reviewed bytes

Source code

Download .py

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

from math import exp,sqrt
E=exp(1)
def P():input("[enter]");print("\n"*11)
def V(s):
 s=s.strip()
 if s=="e":return E
 if s.startswith("sqrt(") and s.endswith(")"):return sqrt(V(s[5:-1]))
 if "/" in s:a,b=s.split("/",1);return V(a)/V(b)
 return float(s)
def N(p):
 while 1:
  try:
   v=V(input(p).lower().replace(" ",""))
   if v-v:raise ValueError
   return v
  except (ValueError,ZeroDivisionError):print("Enter a number")
def B():
 while 1:
  try:
   b=V(input("Base b? ").lower().replace(" ",""))
   if b>0 and b!=1 and b-b==0:return b
  except (ValueError,ZeroDivisionError):pass
  print("b>0, not 1. Like:\n2  1/2  sqrt(2)  e")
def F(x):
 if abs(x-round(x))<1e-9:return str(int(round(x)))
 for d in range(2,101):
  n=round(x*d)
  if abs(x-n/d)<1e-8:return str(n)+"/"+str(d)
 return str(round(x,4))
def get():
 a=N("a? ");b=B();h=N("h? ");k=N("k? ")
 s=-1 if input("Flip x inside? 1 No 2 Yes ").strip()=="2" else 1
 print("\n"*11);return a,b,h,k,s
def pts(L):
 print("5 PLOT POINTS")
 for x,y in L:print("("+F(x)+", "+F(y)+")")
 P()
def ex():
 print("y=a*b^(+/-[x-h])+k")
 a,b,h,k,s=get()
 pts([(h+s*t,a*b**t+k) for t in(-2,-1,0,1,2)])
 print("ASYMPTOTE: y = "+F(k)+"\nDOMAIN: (-inf, inf)")
 print("RANGE: "+("("+F(k)+", inf)" if a>0 else "(-inf, "+F(k)+")" if a<0 else "y = "+F(k)));P()
def lg():
 print("y=a*log_b(+/-[x-h])+k")
 a,b,h,k,s=get()
 pts([(h+s*b**t,a*t+k) for t in(-2,-1,0,1,2)])
 print("ASYMPTOTE: x = "+F(h))
 print("DOMAIN: "+("("+F(h)+", inf)" if s==1 else "(-inf, "+F(h)+")")+"\nRANGE: (-inf, inf)");P()
print("Exp/Log Points\n      __\n  ___(o )> quack!\n  \\ <_. )\n   `---'\n  by DuckieDai\nhiddenwordscanner.com");P()
while 1:
 c=input("1 Exponential\n2 Logarithmic\n3 Quit\nChoice? ").strip();print("\n"*11)
 try:
  if c=="1":ex()
  elif c=="2":lg()
  elif c=="3":break
 except (OverflowError,ValueError):print("Too large");P()

from math import exp,sqrt
E=exp(1)
def P():input("[enter]");print("\n"*11)
def V(s):
s=s.strip()
if s=="e":return E
if s.startswith("sqrt(") and s.endswith(")"):return sqrt(V(s[5:-1]))
if "/" in s:a,b=s.split("/",1);return V(a)/V(b)
return float(s)
def N(p):
while 1:
try:
v=V(input(p).lower().replace(" ",""))
if v-v:raise ValueError
return v
except (ValueError,ZeroDivisionError):print("Enter a number")
def B():
while 1:
try:
b=V(input("Base b? ").lower().replace(" ",""))
if b>0 and b!=1 and b-b==0:return b
except (ValueError,ZeroDivisionError):pass
print("b>0, not 1. Like:\n2 1/2 sqrt(2) e")
def F(x):
if abs(x-round(x))<1e-9:return str(int(round(x)))
for d in range(2,101):
n=round(x*d)
if abs(x-n/d)<1e-8:return str(n)+"/"+str(d)
return str(round(x,4))
def get():
a=N("a? ");b=B();h=N("h? ");k=N("k? ")
s=-1 if input("Flip x inside? 1 No 2 Yes ").strip()=="2" else 1
print("\n"*11);return a,b,h,k,s
def pts(L):
print("5 PLOT POINTS")
for x,y in L:print("("+F(x)+", "+F(y)+")")
P()
def ex():
print("y=a*b^(+/-[x-h])+k")
a,b,h,k,s=get()
pts([(h+s*t,a*b**t+k) for t in(-2,-1,0,1,2)])
print("ASYMPTOTE: y = "+F(k)+"\nDOMAIN: (-inf, inf)")
print("RANGE: "+("("+F(k)+", inf)" if a>0 else "(-inf, "+F(k)+")" if a<0 else "y = "+F(k)));P()
def lg():
print("y=a*log_b(+/-[x-h])+k")
a,b,h,k,s=get()
pts([(h+s*b**t,a*t+k) for t in(-2,-1,0,1,2)])
print("ASYMPTOTE: x = "+F(h))
print("DOMAIN: "+("("+F(h)+", inf)" if s==1 else "(-inf, "+F(h)+")")+"\nRANGE: (-inf, inf)");P()
print("Exp/Log Points\n __\n ___(o )> quack!\n \\ <_. )\n `---'\n by DuckieDai\nhiddenwordscanner.com");P()
while 1:
c=input("1 Exponential\n2 Logarithmic\n3 Quit\nChoice? ").strip();print("\n"*11)
try:
if c=="1":ex()
elif c=="2":lg()
elif c=="3":break
except (OverflowError,ValueError):print("Too large");P()

Filename: PLOT.py
Size: 1857 bytes
SHA-256: 87d7c33e525b12b637608657182b57af198deb0c31b8ddbf03bc5e99752028a6

Usage

Inputs

1 for exponential y = a*b^(x-h)+k or 2 for logarithmic y = a*log_b(x-h)+k
a, the base b, h, and k, as numbers, fractions, sqrt( ), or e
Whether x is reflected inside, as in b^-(x-h) or log_b(-(x-h))

Outputs

Five plot points, from the key points of the parent graph
The asymptote, y = k or x = h
The domain and range

Units: Function parameters; no physical units.

Assumptions and limitations

Assumptions

The function is in the form shown on the menu, with the shift inside written as x-h.
Points come from the parent graph's exponents -2 to 2, so they are easy to plot.

Constraints

The base must be greater than 0 and not 1; inf and nan are asked for again.
Values are shown as whole numbers, fractions with bottoms up to 100, or decimals to four places.

Known failures

Numbers too large for the calculator show Too large and return to the menu.
When a is 0 the graph is a flat line, but the program still lists an asymptote.

Compatibility and review

Review status: Owner-tested on a TI calculator
Tested on: Owner reports personally running this program on a TI-84 Plus CE Python calculator; the test date, OS version, and Python App version were not recorded
What happened: Owner reported pass on the calculator before two changes: the number and base prompts now ask again when inf or nan is typed, and a result too large for the calculator now shows Too large and returns to the menu, where the original stopped with an error. Every other step is unchanged; this exact file has not yet been rerun on a calculator.
Dependencies: math
Suggested calculator name: PLOT — 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

Download the .py file, send it to your calculator with TI Connect CE as PLOT or another name, then open the Python App and try the worked example on this page first. This release has no verified calculator OS or Python App version; treat transfer and execution as unverified until independently tested.

Full installation and troubleshooting guide. Check your teacher's or exam's rules before using any program.

Version history

1.0.0 — current version, published 2026-10-22. Download this reviewed version

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