The function f(x) = 5x + 4 is a linear function, which means its graph is a straight line. To sketch the graph, we can find two points by choosing different values for x.
Let’s find the y-intercept (where the line crosses the y-axis) by setting x to 0:
- f(0) = 5(0) + 4 = 4
This gives us the point (0, 4).
Now, let’s choose another value for x; let’s use x = 1:
- f(1) = 5(1) + 4 = 9
This gives us the point (1, 9).
Now we have two points: (0, 4) and (1, 9). We can plot these points on a graph and draw a straight line through them to represent the function.
In terms of the domain and range:
- The domain of f(x) = 5x + 4 is all real numbers, denoted as (-∞, ∞), because you can substitute any real number for x.
- The range is also all real numbers, (-∞, ∞), because as x takes on all real values, f(x) will also generate all real numbers since it is a linear function that extends infinitely in both directions.
In conclusion, the graph is a straight line that crosses the y-axis at (0, 4) and it has a slope of 5. The domain and range for the function f(x) = 5x + 4 are both all real numbers.