Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. \( h(x)=2 x \)

To graph the linear function \( h(x) = 2x \), we can start by identifying some key points. This function is a linear function with a slope of 2 and a y-intercept of 0. ### Key Points: 1. When \( x = 0 \): \[ h(0) = 2(0) = 0 \quad \text{(Point: (0, 0))} \] 2. When \( x = 1 \): \[ h(1) = 2(1) = 2 \quad \text{(Point: (1, 2))} \] 3. When \( x = -1 \): \[ h(-1) = 2(-1) = -2 \quad \text{(Point: (-1, -2))} \] ### Graph: To graph the function, plot the points (0, 0), (1, 2), and (-1, -2) on a coordinate plane. Then, draw a straight line through these points, extending in both directions. ### Domain and Range: - **Domain**: The domain of a linear function is all real numbers, since you can input any real number for \( x \). Therefore, the domain is: \[ \text{Domain: } (-\infty, \infty) \] - **Range**: Similarly, the range of a linear function is also all real numbers, as the output \( h(x) \) can take any real value. Therefore, the range is: \[ \text{Range: } (-\infty, \infty) \] ### Conclusion: The function \( h(x) = 2x \) is not a constant function; it is a linear function with a slope of 2. - **Domain**: \( (-\infty, \infty) \) - **Range**: \( (-\infty, \infty) \)