1. The problem asks to graph three different functions and determine several properties: x-intercepts, y-intercepts, domain, range, maxima or minima, and the number of solutions. 2. Since the functions are not specified, let's illustrate with three sample functions: 1) $$f(x) = x^2 - 4$$ 2) $$g(x) = \sin(x)$$ 3) $$h(x) = \frac{1}{x}$$ 3. For each function, we analyze as follows: **Function 1: $$f(x) = x^2 - 4$$** - X-intercepts where $$f(x) = 0$$: $$x^2 - 4 = 0 \Rightarrow x^2 = 4 \Rightarrow x = \pm 2$$ So, intercepts at $(-2,0)$ and $(2,0)$. - Y-intercept where $$x=0$$: $$f(0) = 0^2 - 4 = -4$$ So, y-intercept at $(0,-4)$. - Domain: $$\text{All real numbers } (-\infty, \infty)$$ - Range: Since it is a parabola opening upwards with vertex at $(0,-4)$, range is $$[-4, \infty)$$ - Minimum point: Vertex at $(0,-4)$ is the minimum point. - Number of solutions to $$f(x) = 0$$: Two solutions, $x = -2, 2$. **Function 2: $$g(x) = \sin(x)$$** - X-intercepts: $$\sin(x)=0 \implies x = n\pi, n \in \mathbb{Z}$$ - Y-intercept: $$g(0) = 0$$ - Domain: All real numbers $(-\infty, \infty)$ - Range: $$[-1,1]$$ - Maxima and minima: Max at $(\frac{\pi}{2} + 2n\pi, 1)$ Min at $(\frac{3\pi}{2}+ 2n\pi, -1)$ - Number of solutions to $$g(x) = 0$$: Infinitely many solutions at integer multiples of $\pi$. **Function 3: $$h(x) = \frac{1}{x}$$** - X-intercept: Solve $$\frac{1}{x} = 0$$ no solution (function never zero). - Y-intercept: Undefined at $x=0$, so no y-intercept. - Domain: $$(-\infty, 0) \cup (0, \infty)$$ - Range: $$(-\infty, 0) \cup (0, \infty)$$ - No maxima or minima. - Number of solutions to $$h(x)=0$$: Zero solutions. 4. To graph these, use any graphing tool like DESMOS or GeoGebra by entering the respective functions. 5. Printing: After graphing, use the print or export function in the app to obtain a physical or digital copy. These steps help understand key properties of different function types and how technology aids graphing and analysis.