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Core Connections Integrated I, 2013

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Core Connections Integrated I, 2013 View details

2. Section 11.2

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Exercise 75 Page 611

To graph the first function you need to use a value table.

Diagram:

Solution: $x \approx 1.3$

Practice makes perfect

To graph the second function — which is a straight line — we should plot the $y -$ intercept and then use the slope to plot a second point through which the line passes. When we have two points through which the function passes, we can draw its graph.

To graph the first function we need to make a value table.

x - 1 0123 - (\frac{1}{3})^{x} - (\frac{1}{3})^{- 1} - (\frac{1}{3})^{0} - (\frac{1}{3})^{1} - (\frac{1}{3})^{2} - (\frac{1}{3})^{3} y - 3 - 1 \approx - 0.33 \approx - 0.11 \approx - 0.04

Now we can draw the second function on the same set of axes.

Examining the diagram, we see that the functions intersect at roughly

x = 1.3 .

To check our solution, we will calculate

f (x)

and

g (x)

for values of

x

starting from

1 .

x 1 1.1 1.2 1.3 1.4 - 2.5 x + 3 0.50 0.25 0 - 0.25 - 0.50 - (\frac{1}{3})^{x} \approx - 0.33 \approx - 0.30 \approx - 0.27 \approx - 0.24 \approx - 0.21

As we can see, when

x \approx 1.3

the functions intersect.

Subchapter links

11.2.1 Solving Work and Mixture Problems p.603-604

11.2.2 Solving Equations and Systems Graphically p.607-608

11.2.3 Using a Best-Fit Line to Make a Prediction p.610-614

11.2.4 Treasure Hunt p.616-617

11.2.5 Using Coordinate Geometry and Constructions to Explore Shapes p.620-621

11.2.6 Modeling with Exponential Functions and Linear Inequalities p.625-628