F(x)=2x+4

The function you provided is a linear function:

\[ f(x) = 2x + 4 \]

Characteristics of the Function:

1. Slope (m): The coefficient of \(x\) is 2. This means the slope of the line is 2, indicating that for every unit increase in \(x\), \(f(x)\) increases by 2 units.

2. Y-intercept (b): The constant term is 4. This means that the line crosses the y-axis at the point (0, 4).

3. Domain: The domain of this function is all real numbers, written as \((-\infty, \infty)\).

4. Range: The range of this function is also all real numbers, \((-\infty, \infty)\), since it is a linear function and can take any real value.

Graphing the Function:

To graph the function, you can start by plotting the y-intercept at (0, 4). Then, using the slope, you can find another point. For example, if you increase \(x\) by 1 (to 1), \(f(1) = 2(1) + 4 = 6\). This gives you another point (1, 6). You can connect these points with a straight line.

Finding Specific Values:

You might also want to evaluate the function for specific values:

• \(f(0) = 2(0) + 4 = 4\)
• \(f(1) = 2(1) + 4 = 6\)
• \(f(-1) = 2(-1) + 4 = 2\)

Solving for \(x\):

If you want to find \(x\) for a particular value of \(f(x)\):

• If \(f(x) = 10\), set up the equation: \[ 10 = 2x + 4 \] Subtract 4 from both sides: \[ 6 = 2x \] Divide by 2: \[ x = 3 \]

Let me know if you need any more specific information about this function or its applications!