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Big Ideas Math Integrated I, 2016 View details

1. Exponential Functions

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Exercise 53 Page 280

Start by making a table of values for both functions.

Graph:

Table:

Function	y-intercept	Domain	Range
f(x)=- 2^x	(0, - 1)	All real numbers	y< 0
g(x)=- 2^x-3	(0, - 4)	All real numbers	y< - 3

Practice makes perfect

We want to draw graphs of the exponential functions. ccc f(x)=- 2^x & & & g(x)=- 2^x-3 To do so, we will first make a table of values.

x	- 1	0	1	2
f(x)=- 2^x	- 2^(- 1)= - 1/2	- 2^0= - 1	- 2^1= - 2	- 2^2= - 4
g(x)=- 2^x-3	- 2^(- 1)-3= - 3 1/2	- 2^0-3= - 4	- 2^1-3= - 5	- 2^2-3= - 7

The ordered pairs ( - 3, - 18), ( 0, - 1), and ( 3, - 8) all lie on the function f(x)=- 2^x.
The ordered pairs ( - 3, - 3 18), ( 0, - 4), and ( 3, - 11) all lie on the function g(x)=- 2^x-3.

Now, we will plot and connect these points with a smooth curve.

We see that g(x)=- 2^x-3 is a vertical translation of f(x)=- 2^x down by 3 units. Hence, the y-intercept of g is 3 units below the y-intercept of f. Both functions have the same domain — all real numbers. The range of f is y< 0, and the range of g is y < - 3. Let's show them in a table.

Function	y-intercept	Domain	Range
f(x)=- 2^x	(0, - 1)	All real numbers	y< 0
g(x)=- 2^x-3	(0, - 4)	All real numbers	y< - 3

Subchapter links

Communicate Your Answer p.273

Monitoring Progress p.274-277

Exercises p.278-280

Exercise 53 Page 280

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