Montana Math MT.PLUS.ALG.EXP.4

MathGrades 9–12Exponential and Logarithmic Functions

The Standard

Graph logarithmic and exponential functions with and without the use of technology by identifying intercepts, asymptotes, and end behavior.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students sketch exponential and logarithmic graphs by hand and with a graphing tool. They label intercepts and asymptotes, then describe what happens at each end of the graph.
What Mastery Looks Like: They sketch y=2^x with a y-intercept at (0,1), no x-intercept, and asymptote y=0. They sketch y=log_2(x) with an x-intercept at (1,0), no y-intercept, and asymptote x=0. They describe what happens as x increases and as each graph approaches its asymptote.
Common Misconceptions: Students may draw an exponential graph crossing its horizontal asymptote. They may put a logarithmic graph on the y-axis, even though its input must be positive. Some assume an asymptote stays on an axis when the graph shifts.
How to Assess It: Exit ticket: Sketch y=2^x and y=log_2(x) without a calculator. Label their intercepts and asymptotes, write “none” where needed, and describe what happens at both ends.

Lesson moves

Place ordered-pair cards for y=2^x on a floor grid, swap coordinates to build y=log_2(x), and mark each asymptote with tape.
Ask students to write why y=log_2(x) has no y-intercept while y=2^x does, using the graphs to support their answer.
Give pairs printed graphs and function cards, including y=3^x and y=log_3(x-2); have them match the cards, then check with a graphing tool.
Graph a $100 deposit growing at 5% yearly and its inverse, then discuss why the graphs extend beyond the time and balances in the savings example.

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