Question

sara wants to find the input value that produces the same output for the functions represented by the tables. for ( f(x) = -0.5x + 2 ), the table has ( x ) values -3, -2, -1, 0, 1, 2, 3 with corresponding ( f(x) ) values 3.5, 3, 2.5, 2, 1.5, 1, 0.5. for ( g(x) = 2x - 3 ), the table has ( x ) values -3, -2, -1, 0, 1, 2, 3 (with ( g(x) ) values to be filled). the question is: what is the input value that produces the same output value in both charts? the options are 2, 1, -2, -1.

Explanation:

Step1: Set the functions equal

To find the input \( x \) where \( f(x) = g(x) \), set \( -0.5x + 2 = 2x - 3 \).

Step2: Solve for \( x \)

Add \( 0.5x \) to both sides: \( 2 = 2.5x - 3 \).
Add 3 to both sides: \( 5 = 2.5x \).
Divide by 2.5: \( x = \frac{5}{2.5} = 2 \).
Check with tables: For \( f(2) = -0.5(2) + 2 = 1 \), for \( g(2) = 2(2) - 3 = 1 \). Both outputs are 1 when \( x = 2 \).

Answer:

2