Question

which graph represents the function f(x)=2x - 1?

Explanation:

Step1: Analyze the function type

The function \( f(x) = 2x - 1 \) is a linear function in the form \( y = mx + b \), where \( m = 2 \) (slope) and \( b = - 1 \) (y - intercept).

Step2: Determine key points

• Y - intercept: When \( x = 0 \), \( f(0)=2(0)-1=-1 \), so the graph passes through the point \( (0, - 1) \).
• X - intercept: When \( y = 0 \), \( 0 = 2x-1\), solving for \( x \) gives \( x=\frac{1}{2} \), so the graph passes through the point \( (\frac{1}{2},0) \).
• Slope interpretation: The slope \( m = 2 \) means that for every 1 unit increase in \( x \), \( y \) increases by 2 units. So the graph should be a straight line with a positive slope, crossing the y - axis at \( (0,-1) \) and the x - axis at \( (\frac{1}{2},0) \).

Step3: Match with the graph

We need to look for a straight line that has a positive slope, passes through \( (0, - 1) \) and \( (\frac{1}{2},0) \). (Since the actual graphs are not shown here, but in general, among the given graph options, we check for these characteristics)

Answer:

(The answer would be the graph that is a straight line with positive slope, passing through (0, - 1) and (1/2, 0). If the options are labeled as A, B, C, D etc., we would identify the correct one based on the above - mentioned characteristics. For example, if option A has these characteristics, the answer would be A. [Graph with positive slope, y - intercept - 1, x - intercept 1/2])