What is "if f(x) = 6x – 4?

The expression "f(x) = 6x – 4" defines a linear function. Here's what we know about it:

• Type of Function: It's a linear function because the highest power of x is 1. This means its graph will be a straight line.

• Slope: The slope of the line is 6. This represents the rate of change of f(x) with respect to x. For every 1 unit increase in x, f(x) increases by 6 units.

• Y-intercept: The y-intercept is -4. This is the point where the line crosses the y-axis (where x = 0). Therefore, f(0) = -4.

• Graph: The graph will be a straight line with a positive slope (sloping upwards from left to right) that intersects the y-axis at the point (0, -4).

• Domain and Range: The domain (all possible x values) and range (all possible f(x) values) are both all real numbers (-∞, ∞). This is because you can plug in any real number for x and get a real number output.

• Finding Values: To find the value of the function at a specific x, you simply substitute that value into the equation. For example:

  • f(1) = 6(1) - 4 = 2
  • f(2) = 6(2) - 4 = 8
  • f(-1) = 6(-1) - 4 = -10

In short, f(x) = 6x - 4 describes a simple linear relationship where the output (f(x)) is directly proportional to the input (x), with a constant rate of change and a specific starting point.