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PSAT · Question of the Day

PSAT Question of the Day

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Monday, September 21, 2026

A coordinate plane graph shows an exponential curve that passes through (0,1)(0,1) and increases to the right. It also appears to pass near (1,2)(1,2) and (2,4)(2,4). Which equation best matches the graph? (If the scale is misread, 2x2^x and 3x3^x can look similar for small xx.)

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Question of the Day

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A coordinate plane graph shows an exponential curve that passes through (0,1)(0,1) and increases to the right. It also appears to pass near (1,2)(1,2) and (2,4)(2,4). Which equation best matches the graph? (If the scale is misread, 2x2^x and 3x3^x can look similar for small xx.)

  1. y=3xy=3^x
  2. y=2xy=2^x (correct answer)
  3. y=(12)xy=\left(\tfrac12\right)^x
  4. y=2x−1y=2^{x-1}

Explanation: The question seeks the equation for an exponential graph passing through (0,1), increasing rightward, and near (1,2) and (2,4). The curve starts at y=1 on the y-axis, rises steeply to the right, and shows growth consistent with base greater than 1, without a horizontal asymptote visible above y=0. Evaluating y = 2^x gives 2^0 = 1, 2^1 = 2, and 2^2 = 4, aligning perfectly with the points and connecting the visual growth to the exponential base. For comparison, y = 3^x at x=1 is 3, overshooting the near-point at 2. A common error is misreading the scale, confusing 2^x with 3^x for small x, or selecting decaying functions like C. Another mistake is choosing shifted versions like D, which passes through (0,0.5). To verify exponentials, check key points like the y-intercept and integer inputs against the graph.