1. **Problem statement:** We need to graph two functions using the point plotting method for integer values of $x$ from $-3$ to $3$. 2. **Graph 1: $y = 4 - x^2$** - This is a parabola opening downward because of the negative coefficient on $x^2$. - We will calculate $y$ values for each integer $x$ from $-3$ to $3$. | $x$ | $y=4 - x^2$ | |-----|------------| | -3 | $4 - (-3)^2 = 4 - 9 = -5$ | | -2 | $4 - (-2)^2 = 4 - 4 = 0$ | | -1 | $4 - (-1)^2 = 4 - 1 = 3$ | | 0 | $4 - 0^2 = 4 - 0 = 4$ | | 1 | $4 - 1^2 = 4 - 1 = 3$ | | 2 | $4 - 2^2 = 4 - 4 = 0$ | | 3 | $4 - 3^2 = 4 - 9 = -5$ | 3. **Graph 2: $y = 1x$ or $y = x$** - This is a straight line passing through the origin with slope 1. - Calculate $y$ for integer $x$ values from $-3$ to $3$: | $x$ | $y = x$ | |-----|--------| | -3 | -3 | | -2 | -2 | | -1 | -1 | | 0 | 0 | | 1 | 1 | | 2 | 2 | | 3 | 3 | 4. **Summary of points for plotting:** - Parabola: $(-3,-5), (-2,0), (-1,3), (0,4), (1,3), (2,0), (3,-5)$ - Line: $(-3,-3), (-2,-2), (-1,-1), (0,0), (1,1), (2,2), (3,3)$ These points can be plotted on a Cartesian plane to visualize the parabola and the line. **Final answer:** - The parabola $y = 4 - x^2$ has the shape opening downward with vertices as calculated. - The line $y = x$ passes through the origin with slope 1.