AP Pre-Cal Justifications

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Last updated 3:05 AM on 5/10/26
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25 Terms

1
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f is best modeled by a linear function because…

Over consecutive equal-length input intervals of ___, there is a constant difference in output values of ___.

2
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f is best modeled by a quadratic function because…

Over consecutive equal-length input intervals of ___, there is a constant second difference in output values of ___.

3
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f is best modeled by an exponential function because…

Input values change additively in intervals of ___ as output values change proportionally by a factor of ___.

4
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f is best modeled by a logarithmic function because…

Input values change proportionally by a factor of ___ as output values change additively in intervals of ___.

5
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A function f is invertible because…

Each output value of f is mapped from a unique input value. There are no repeated f(x) values.

6
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The estimated output value found by using a known output and the average rate of change is an overestimate because…

Secant line is above the curve at the input value of the estimate (sketch a picture).

7
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The estimated output value found by using a known output and the average rate of change is an underestimate because…

Secant line is below the curve at the input value of the estimate (sketch a picture).

8
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f is positive because…

The graph of f is above the x/t-axis.

9
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f is negative because…

The graph of f is below the x/t-axis.

10
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f is increasing because…

The graph of f has a positive slope.

11
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f is decreasing because../

The graph of f has a negative slope.

12
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The rate of change of f is increasing because…

f is concave up.

13
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The rate of change of f is increasing because…

f is concave down.

14
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f is concave up because…

The average rate of change of f over equal-length input intervals is increasing.

15
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f is concave down because…

The average rate of change for f over equal-length input intervals is decreasing.

16
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The graph of f has a hole at x = a because…

The multiplicity of x = a in the numerator is greater than or equal to the multiplicity of x = a in the denominator.

17
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The graph of f has a vertical asymptote at x = a because…

x = a is a zero of the denominator and NOT of the numerator.

18
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The graph of f has an x-intercept at x = a because…

x = a is a zero of the numerator and not the denominator.

19
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f has a relative minimum at x = a because…

f changes from increasing to decreasing at x = a.

20
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f has a relative maximum at x = a because…

f changes from decreasing to increasing at x = a.

21
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A model is considered appropriate for a data set because…

The residual plot for the model has no clear pattern.

22
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The value predicted by the model at a certain input gives an overestimate for the true value at that input because…

The residual for that input is negative.

23
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The value predicted by the model at a certain input gives an underestimate for the true value at that input because…

The residual for that input is positive.

24
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The distance between a point on the graph of r = f(θ) and the origin is increasing because…

Values of r are positive and increasing.

25
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The distance between a point on the graph of r = f(θ) and the origin is decreasing because…

Values of r are positive and decreasing.