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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 ___.
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 ___.
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 ___.
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 ___.
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.
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).
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).
f is positive because…
The graph of f is above the x/t-axis.
f is negative because…
The graph of f is below the x/t-axis.
f is increasing because…
The graph of f has a positive slope.
f is decreasing because../
The graph of f has a negative slope.
The rate of change of f is increasing because…
f is concave up.
The rate of change of f is increasing because…
f is concave down.
f is concave up because…
The average rate of change of f over equal-length input intervals is increasing.
f is concave down because…
The average rate of change for f over equal-length input intervals is decreasing.
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.
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.
The graph of f has an x-intercept at x = a because…
x = a is a zero of the numerator and not the denominator.
f has a relative minimum at x = a because…
f changes from increasing to decreasing at x = a.
f has a relative maximum at x = a because…
f changes from decreasing to increasing at x = a.
A model is considered appropriate for a data set because…
The residual plot for the model has no clear pattern.
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.
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.
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.
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.