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Explain Bot To determine which of the given functions is linear, we need to understand what it means for a function to be linear.
A linear function is a function that can be represented by a straight line on a graph. It has the general form of y = mx + b, where m is the slope and b is the y-intercept.
Let's analyze the given options and determine if any of them represent a linear function:
1. f(x) = x^2
This is a quadratic function since it has an x^2 term. Quadratic functions do not represent linear functions because their graphs form a parabola, not a straight line.
2. f(x) = 2x + 3
This is a linear function since it is in the form y = mx + b. The coefficient of x, in this case, is 2, which represents the slope, and the constant term 3 represents the y-intercept. The graph of this function will be a straight line.
3. f(x) = √x
This is a square root function. like the quadratic function, it does not represent a linear function. The graph of a square root function forms a curve, not a straight line.
4. f(x) = 3x^2 + 4x - 2
This is another quadratic function since it contains x^2. Therefore, it does not represent a linear function.
Based on the analysis, the only linear function among the given options is f(x) = 2x + 3.