d) \( f(x)=\frac{2 x}{3}+7-\frac{x}{2} \)

Let's first simplify the function \( f(x) \) step by step. Combining the terms, we have: \[ f(x) = \frac{2x}{3} - \frac{x}{2} + 7 \] To combine \( \frac{2x}{3} \) and \( -\frac{x}{2} \), we need a common denominator, which is 6. Thus, we can rewrite the fractions: \[ \frac{2x}{3} = \frac{4x}{6} \quad \text{and} \quad -\frac{x}{2} = -\frac{3x}{6} \] Now, substituting back into the function: \[ f(x) = \frac{4x}{6} - \frac{3x}{6} + 7 = \frac{x}{6} + 7 \] So, the simplified form of the function is: \[ f(x) = \frac{x}{6} + 7 \] This shows a linear function with a slope of \( \frac{1}{6} \) and a y-intercept at 7, which means it rises gradually! Want to explore how to graph this function? Just plot the y-intercept at (0, 7) and use the slope to find another point (for example, moving up 1 unit and right 6 units).