Subjects algebra

Function Range 326Cac

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

Question: Fill in each blank so that the resulting statement is true. The shaded set of numbers shown on the y-axis on the graph can be expressed in interval notation as _______. This set represents the function's _______. A coordinate system has a horizontal x-axis labeled from negative 5 to 5 in increments of 1 and a vertical y-axis labeled from negative 3 to 15 in increments of 1. The region on the y-axis above a bracket at 1 is shaded. A line labeled $y=f(x)$ that rises from left to right starts at $(-2, 1)$ and passes through the points $(0, 3)$ and $(2, 5)$.
1. **State the problem:** We are given a graph with a function $y=f(x)$ that starts at $(-2,1)$ and passes through $(0,3)$ and $(2,5)$. The shaded region on the y-axis is above the bracket at $1$. 2. **Identify the shaded set on the y-axis:** The shaded region on the y-axis starts at $1$ and extends upwards, including all $y$ values greater than or equal to $1$. 3. **Express the shaded set in interval notation:** Since the shading starts at $1$ and goes to positive infinity, the interval notation is $$[1, \infty)$$. 4. **Determine what this set represents:** The shaded set on the y-axis represents the range of the function $f(x)$ because it shows all possible output values $y$ that the function can take. **Final answers:** - Interval notation: $$[1, \infty)$$ - This set represents the function's **range**.