Identify which of the graphs represents the function 𝑓 of 𝑥 is equal to negative one-half.
We begin by recalling that a linear function is a function of the form 𝑦 is equal to 𝑓 of 𝑥, which is equal to 𝑚𝑥 plus 𝑏, where 𝑚 and 𝑏 are real numbers. 𝑚 represents the slope or gradient of the line, and 𝑏 represents the 𝑦-intercept. In this question, we are told that the function 𝑓 of 𝑥 is equal to the constant negative one-half. This means that 𝑚 is equal to zero, and our constant function is represented graphically by a horizontal line. This line will have a 𝑦-intercept equal to negative one-half and will therefore pass through the point with coordinates zero, negative one-half.
We can see by inspection that the only one of our five graphs that passes through this point is graph (E). This is a horizontal line with slope equal to zero and 𝑦-intercept of negative one-half. And we can therefore conclude that the graph that represents the function 𝑓 of 𝑥 equals negative one-half is graph (E).
It is worth noting that graphs (B), (C), and (D) are not horizontal lines. So we could have immediately eliminated them. And we could also rule out graph (A), as this passes through the point zero, one-half and not zero, negative one-half. Ruling out the other four options confirms that the correct answer is graph (E).