QuestionDraw a function with the following characteristics: a. Continuous b. $x$ -intercepts at $x=2, x=-4$ c. $y$ -intercept at $y=6$ d. Includes the point $(3,1)$ e. Domain: $\{-5<x \leq 4\}$ f. Range: $\{-3 \leq y \leq 6\}$

Studdy Solution

STEP 1

1. The function must be continuous.
2. The function must have $x$ -intercepts at $x = 2$ and $x = -4$ .
3. The function must have a $y$ -intercept at $y = 6$ .
4. The function must pass through the point $(3, 1)$ .
5. The domain of the function is $-5 < x \leq 4$ .
6. The range of the function is $-3 \leq y \leq 6$ .

STEP 2

1. Analyze the given intercepts and point.
2. Consider the domain and range constraints.
3. Sketch a continuous function that satisfies all conditions.

STEP 3

Identify the required intercepts and points: - $x$ -intercepts: $x = 2$ , $x = -4$ - $y$ -intercept: $y = 6$ - Passes through: $(3, 1)$

STEP 4

Consider the domain and range: - Domain: $-5 < x \leq 4$ - Range: $-3 \leq y \leq 6$

STEP 5

Sketch the function: - Start by plotting the $x$ -intercepts at $x = 2$ and $x = -4$ . - Plot the $y$ -intercept at $y = 6$ . - Ensure the function passes through the point $(3, 1)$ . - Ensure the function is continuous and fits within the given domain and range. - Consider using a polynomial or piecewise function that meets these criteria.
The function could be a piecewise function or a polynomial that smoothly transitions through the given points and intercepts, ensuring it remains within the specified domain and range.

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