Algebra 1 Common Core Student Edition, Grade 8-9

In the Concept Byte after Lesson 6-1, you solved one-variable linear equations using

graphs and a graphing calculator. In the next example, you will write each side of

the equation as a function and graph the functions. The x-value where the functions

intersect is a solution.

So l v i n g O n e - V a r i a b l e Eq u a t i o n s

What is the solution or solutions of 2X = 0.5x + 2?

St e p 1 Write each side of the equation as a function equation.

/(x) = 2* and g(x) = 0.5x + 2

St e p 2 Graph the equations using a graphing calculator.

Use jq for f{x) and y2 for g(x).

How can you check
that the x-value is a
so l u t i o n?
Su b st i t u t e f o r x i n t h e
original equation. Make
sur e yo u use t h e sam e
x- val ue f or each inst ance
of x.

St e p 3 Use the CALC feature. Chose

INTERSECT to find the

points where the lines intersect.

Ihe solutions of 2X = 0.5x + 2 are about —3.86 and 1.45.

& Got It? 5. What is the solution or solutions of each equation?

a. 0.3* = 5 b. 1.25*= —2 x C. -(2*) = 4*-4

Lesso n Ch eck

Do y o u k n o w H OW?

Evaluate each function for the given value.

1. /(x) = 6 • 2*forx = 3


2. g(w) = 45 • 3W for w = — 2

Graph each function.

3. y = 3*

4.^) —4(1)'

Do yo u UNDERSTAND? tg jf PRAcflcES

5. Vocabulary Describe the differences between a
   linear function and an exponential function.


6. Reasoning Is y = (-2)* an exponential function?
   Justify your answer.


7. Error Analysis A student evaluated
   the function /(x) = 34
   for x = -1 as shown at the
   right. Describe and correct the
   student's mistake.

456 Ch a p t e r 7 Ex p o n e n t s a n d Ex p o n e n t i a l Fu n c t i o n s