Sara wants to find the input value that produces the same output for the functions represented by the tables.
A table headed with f(x) equals negative 0.5 x plus 2, with 2 columns and 8 rows. The first column, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2, 3. The second row, f(x), has the entries 3.5, 3, 2.5, 2, 1.5, 1, 0.5. A table headed with g(x) equals 2 x minus 3, with 2 columns and 8 rows. The first column, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2, 3. The second row, g(x), has no entries.
What is the input value that produces the same output value in both charts?
–2
–1
1
2
Answers
Answer:
2 is the value that provides the same result with f(x) and g(x).
Step-by-step explanation:
You can solve this by saying:
f(x) = g(x)
and then solving for x.
So let's do it:
[tex]f(x) = g(x)\\-0.5x + 2 = 2x - 3\\2x + 0.5x = 2 + 3\\2.5x = 5\\x = 2[/tex]
This tells us that when x = 2, the two functions will have identical values. Let's try them out to confirm it!
f(x) = -0.5x + 2
f(2) = -0.5 * 2 + 2
f(2) = -1 + 2
f(2) = 1
g(x) = 2x - 3
g(2) = 2 * 2 - 3
g(2) = 4 - 3
g(2) = 1
So we can see that 2 is the value that produces the same result in both charts.
The input value that produces the same output value in both charts is 2. so the correct answer is option D.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
here, we have,
You are given two functions f (x) = -0.5X +2 and g(x) = 2x - 3
x f(x)
-3 3.5
-2 3
-1 2.5
0 2
1 1.5
2 1
3 0.5
The second table is given below:-
x g(x)
-3
-2
-1
0
1
2
3
We will put the points and will find the value of functions:-
g(-3) = 2(-3) - 3 = -6 -3 = -9
g(-2) = 2 -(-2) -3 = -7
g(-1) = 2( -1) -3 = -3
g(0) = 2 - 0 - 3 = -3
g(1) = 2.1 - 3 = -1
g(2) = 2.2 -3 = 1
g(3) = 2.3 -3 = 3
Hence the second table will be
x g(x)
-3 -9
-2 -7
-1 -5
0 -3
1 -1
2 1
3 3
The input value that produces the same output value in both charts is 2.
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