There are 6 recognisable ways a child goes wrong here — distinct patterns, not carelessness.
Each one below is a mistake our question bank was built to expose, written out the way you would actually hear it said out loud at home.
Knowing which one you are looking at is the whole job. "Check your answer" does not help a child who is confidently applying the wrong rule.
What you might hear"It has an exponent, so the line goes up."
Sees a base between 0 and 1, like y=(1/2)^x, and still draws or expects a curve that goes up to the right.
The child learned that exponential functions grow fast, so they apply that to every base without checking if the base is less than 1.
This one responds to correction in the moment — the idea is there, the rule being applied is not.
What you might hear"It went up by 2, so the next one goes up by 2 again."
Treats an exponential like a line: thinks each equal step in x adds a fixed amount to y instead of multiplying y by the base.
The child is used to linear graphs where you add the slope each step, so they keep adding a constant instead of multiplying.
This one responds to correction in the moment — the idea is there, the rule being applied is not.
What you might hear"4 is bigger, so its curve must be more gentle."
Assumes a larger base, like 4, makes a flatter or slower-rising curve than a smaller base, like 2.
The child guesses about steepness without comparing actual values, or confuses base size with the flattening they see near the left side.
This one responds to correction in the moment — the idea is there, the rule being applied is not.
What you might hearI plotted the points and just drew a line through them, like we always do.
The student connects the points of y=ab^x with a ruler and draws a straight line, treating the base like a slope. They graph y=2^x as a line through (0,1) and (1,2) and keep going straight instead of letting it curve and bend upward.
Most graphs the student has drawn so far were lines. They see a rule with x and assume each step adds the same amount, so they pick a constant slope. But here each step multiplies by the base, so the rise keeps getting bigger and the graph has to curve.
Words rarely shift this one. It needs something to look at — a picture, a fold, an object on the table — before the explanation lands.
What you might hearIt starts at zero, right? And the y-intercept is just the base, 2.
The student thinks y=2^x passes through the origin, so they read the y-intercept as (0,0). Or for y=3*2^x they say the y-intercept is (0,2) because the base is 2, mixing up the base with the starting value.
The student forgets that any base to the power 0 equals 1, so 2^0 is 1, not 0. They also confuse the base (the number being multiplied) with the y-intercept (the value when x=0). For y=a*b^x the y-intercept is a, the value at x=0.
This one responds to correction in the moment — the idea is there, the rule being applied is not.
What you might hearOn the left side I just brought the line down and crossed the x-axis.
The student draws y=2^x or a decay curve dipping below and crossing the x-axis. They miss the horizontal asymptote at y=0 and let the graph touch or cut through the x-axis instead of leveling off just above it.
The student treats the x-axis like any other line the graph can cross. They do not yet see that 2^x is always a positive number, so the y-value gets tiny but never reaches 0. The x-axis is a wall the curve hugs but never touches.
Words rarely shift this one. It needs something to look at — a picture, a fold, an object on the table — before the explanation lands.
For each mistake above, Algo School gives you the words to say next — the specific response that corrects the thinking instead of just marking the answer wrong, plus practice aimed at that exact error.
See your child's own results — start freeRefer to the graph of the exponential function f drawn on the grid. What is the y-intercept of the exponential curve? Which choice is correct?
Answer C — (0, 0)
Generated by graph-functions-alg1, a deterministic question engine — not written by an AI, and verified before any child sees it.
Look at what they SAY, not just what they wrote. Each mistake above includes the phrasing a parent typically hears — that sentence is usually the giveaway. In Algo School, the tutor recognises these patterns while your child is working and adapts the session around the one it sees.
Yes. We track 6 distinct approved mistake patterns for this concept, each one written up because it recurs — not because it is unusual. A child making one of them is doing something systematic, which is far easier to fix than random errors.
Respond to the thinking, not the answer. Algo School gives parents the specific wording for each mistake, then generates practice targeted at that error and shows you whether it actually cleared.
They are part of the same content library that drives practice: each one is reviewed and approved before it is used, and the Interpreting Functions questions on this site are checked by an automated verification pass before a child is ever served them.
See the full curriculum map — every Common Core concept we cover, the verified question count, and what a child at this level should know.
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