Sketching the Graph of f(x) = 5x + 4
The function f(x) = 5x + 4 is a linear function, where ‘5’ is the slope and ‘4’ is the y-intercept. To graph this function, follow these steps:
- Identify the y-intercept: The y-intercept occurs when x = 0. Plugging in this value gives us:
f(0) = 5(0) + 4 = 4.
So, the point (0, 4) is on the graph. - Determine another point using the slope: The slope of the line is ‘5’, which means for every 1 unit you move to the right (positive direction in x), the value of f(x) increases by 5 units. Starting from the y-intercept (0, 4), moving right by 1 unit adds 5 units to y:
From (0, 4) to (1, 9). - Plot the points: You can plot the points (0, 4) and (1, 9) on a graph.
- Draw the line: Connect the points with a straight line, extending it in both directions. This represents the function f(x) = 5x + 4.
Domain and Range
For linear functions like this one:
- Domain: The domain of a linear function is all real numbers, as there are no restrictions on the values that x can take. This can be expressed in interval notation as:
- (-
∞, +
∞) - Range: Similarly, the range of a linear function is also all real numbers since the line continues infinitely in both the upward and downward directions. In interval notation, this is also:
- (-
∞, +
∞)
Thus, the domain and range of f(x) = 5x + 4 are both all real numbers.