Questions: Follow the steps for graphing a rational function to graph the function F(x)=(x^2+5x-36)/(x+3). A. F(x)=((x+9)(x-4))/(x+3) (Type your answer in factored form. Do not simplify.) B. F(x) is already in factored form. What is the domain of F(x)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x x ≠ -3 (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. x x < (Type an integer or a simplified fraction.) C. x x ≥ (Type an integer or a simplified fraction.) D. The domain is the set of all real numbers. Write F(x) in lowest terms. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. F(x)= (Simplify your answer.) B. F(X) is already in lowest terms.

$Follow the steps for graphing a rational function to graph the function F(x)=(x^2+5x-36)/(x+3). A. F(x)=((x+9)(x-4))/(x+3) (Type your answer in factored form. Do not simplify.) B. F(x) is already in factored form. What is the domain of F(x)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x x ≠ -3 (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. x x < (Type an integer or a simplified fraction.) C. x x ≥ (Type an integer or a simplified fraction.) D. The domain is the set of all real numbers. Write F(x) in lowest terms. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. F(x)= (Simplify your answer.) B. F(X) is already in lowest terms.$

Transcript text: Follow the steps for graphing a rational function to graph the function $F(x)=\frac{x^{2}+5 x-36}{x+3}$. A. $F(x)=\frac{(x+9)(x-4)}{x+3}$ (Type your answer in factored form. Do not simplify.) B. $F(x)$ is already in factored form. What is the domain of $F(x)$ ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\{x \mid x \neq-3\}$ (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. $\{x \mid x<\quad\}$ (Type an integer or a simplified fraction.) C. $\{x \mid x \geq \quad\}$ (Type an integer or a simplified fraction.) D. The domain is the set of all real numbers. Write $F(x)$ in lowest terms. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $F(x)=$ $\square$ (Simplify your answer.) B. $F(X)$ is already in lowest terms.

Solution

Solution Steps

Step 1: Factor the numerator of the function

The given function is $ F(x) = \frac{x^2 + 5x - 36}{x + 3} $. We need to factor the numerator $ x^2 + 5x - 36 $.

The factors of $-36$ that add up to $5$ are $9$ and $-4$. Therefore, the numerator can be factored as: \[ x^2 + 5x - 36 = (x + 9)(x - 4) \]

Step 2: Write the function in factored form

The function in factored form is: \[ F(x) = \frac{(x + 9)(x - 4)}{x + 3} \]

Step 3: Determine the domain of the function

The domain of $ F(x) $ is all real numbers except where the denominator is zero. The denominator $ x + 3 = 0 $ when $ x = -3 $. Therefore, the domain is: \[ \{x \mid x \neq -3\} \]

Step 4: Simplify the function to its lowest terms

Since the numerator and denominator do not have any common factors, the function is already in its lowest terms.

Final Answer

The function in factored form is $ F(x) = \frac{(x + 9)(x - 4)}{x + 3} $.
The domain of $ F(x) $ is $ \{x \mid x \neq -3\} $.
The function is already in its lowest terms.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = (x^2 + 5x - 36)/(x + 3)"], "latex_expressions": ["$F(x) = \\frac{x^2 + 5x - 36}{x + 3}$"]}

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