Question 1

Which graph best represents the exponential function $$f(x) = 2^x$$ and its horizontal reflection $$g(x) = 2$$^{-x}$$?

Accepted Answer

The first image, where $$f(x)$$ increases rapidly for positive $$x$$ and $$g(x)$$ increases rapidly for negative $$x.$$

Question 2

In the first image, what is the relationship between $$f(x)$$ and $$g(x)$$?

Accepted Answer

$$g(x) is $$the horizontal reflection of $$f(x)$$ across the $$y-$$axis.

Question 3

Which image shows the effect of changing the growth factor $$b in $$the exponential function $$f(x) = b^x$$ while keeping the initial value $$a$$ constant?

Accepted Answer

The second image, where several curves pass through the same point but have different steepness.

Question 4

In the third image, what transformation is illustrated by the set of exponential graphs?

Accepted Answer

Changing the initial value $$a in$$ $$f(x) = a b^x$$ while keeping $$b$$ constant.

Question 5

Which image best illustrates the effect of a vertical shift on an exponential function, resulting in a new horizontal asymptote?

Accepted Answer

The fourth image, where the curves have horizontal asymptotes at different $$y$$ values.

Question 6

In the context of exponential functions, what does a horizontal shift correspond to?

Accepted Answer

A change in the initial value $$a of $$the function.

Question 7

Which image shows the intersection of two linear functions, representing a break-even point in a business scenario?

Accepted Answer

The tenth image, where two lines intersect at a single point.

Question 8

In the eleventh image, what does the intersection point of the two lines represent?

Accepted Answer

The solution to the system of equations, where both equations are satisfied.

Question 9

Which image illustrates the solution set to a linear inequality, where the shaded region represents all possible solutions?

Accepted Answer

The fourteenth image, where a region is shaded above a line.

Question 10

In the sixteenth image, what does the overlapping shaded region represent?

Accepted Answer

The solution set to a system of linear inequalities.

Exponential and Logarithmic Functions: Graphs and Properties

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