Question

Select the correct answer from each drop-down menu.

Observe the given functions.


Graph shows a curve and a line plotted on a coordinate plane. The line f begins from (0, 3) and pass through (4, 19). The curve g begins from (0, 1), pass through (3.5, 6) and (5.5, 16).
Complete the sentences to compare the two functions.

Over the interval
, the average rate of change of g is greater than the average rate of change of f.

As the value of x increases, the average rates of change of f and g
, respectively.

When the value of x is equal to 7, the value of
.

It can be further generalized that a quantity increasing exponentially will
exceed a quantity increasing linearly.

Answer 1

The average rate of change of g is greater than the average rate of change of f over the interval [0, 4]. As x increases, the average rates of change of f and g decrease and approach the slope of the line. A quantity increasing exponentially will always exceed a quantity increasing linearly.

Over the interval [0, 4], the average rate of change of g is greater than the average rate of change of f.

As the value of x increases, the average rates of change of f and g decrease and approach the slope of the line.

When the value of x is equal to 7, the value of f is not specified in the provided information.

It can be further generalized that a quantity increasing exponentially will always exceed a quantity increasing linearly.

Answer 2

Explanation:

The absence of a graph or equations makes this a bit tricky. Two equations that approximate the points given are:

f(x) = 4x + 3

g(x) = 2^(1.5) - 2x + 1

See the attached graph.

Over the interval [NOT GIVEN], the average rate of change of g is greater than the average rate of change of f. [Determine the specified interval and compare the two lines]

As the value of x increases, the average rates of change of f and g

, respectively. The rate of change of f is constant. It does not change. The rate of change for g is exponential.

When the value of x is equal to 7, the value of g is 31 A

.

It can be further generalized that a quantity increasing exponentially will

exceed a quantity increasing linearly. Yes, for positive exponents. A change in x of 2 will increase at a constant rate for a linear function. A change of 2 for a function having x^2 will change it by a factor of 4, nonlinear.