Questions: Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of (y=f(x)). [ f(x)=frac1x^2-3 x-18 ] Find the domain of (f(x)). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is all real (x), except (x=6,-3). (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The domain is all real (x). Find the (x)-intercepts of (f(x)). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The (x)-intercept(s) is/are at (x=) (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no (x)-intercepts. Find the (y)-intercepts of (f(x)). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The (y)-intercept(s) is/are at (y=) . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no (y)-intercepts.

Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of (y=f(x)). [ f(x)=frac1x^2-3 x-18 ] Find the domain of (f(x)). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is all real (x), except (x=6,-3). (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The domain is all real (x). Find the (x)-intercepts of (f(x)). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The (x)-intercept(s) is/are at (x=) (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no (x)-intercepts. Find the (y)-intercepts of (f(x)). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The (y)-intercept(s) is/are at (y=) . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no (y)-intercepts.
Transcript text: Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of $y=f(x)$. \[ f(x)=\frac{1}{x^{2}-3 x-18} \] Find the domain of $\mathrm{f}(\mathrm{x})$. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is all real $x$, except $x=6,-3$. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The domain is all real $x$. Find the $x$-intercepts of $f(x)$. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $x$-intercept(s) is/are at $x=$ $\square$ (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no $x$-intercepts. Find the $y$-intercepts of $\mathrm{f}(\mathrm{x})$. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $y$-intercept(s) is/are at $y=$ $\square$ . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no $y$-intercepts.
failed

Solution

failed
failed

Solution Steps

Step 1: Find the Domain of \( f(x) \)

To find the domain of \( f(x) = \frac{1}{x^2 - 3x - 18} \), we need to determine where the denominator is not equal to zero.

Set the denominator equal to zero and solve for \( x \): \[ x^2 - 3x - 18 = 0 \]

Factoring the quadratic equation: \[ (x - 6)(x + 3) = 0 \]

The solutions are \( x = 6 \) and \( x = -3 \). Therefore, the domain of \( f(x) \) is all real numbers except \( x = 6 \) and \( x = -3 \).

Step 2: Find the \( x \)-Intercepts of \( f(x) \)

The \( x \)-intercepts occur where \( f(x) = 0 \). Since \( f(x) = \frac{1}{x^2 - 3x - 18} \), the numerator is always 1, which is never zero. Therefore, there are no \( x \)-intercepts.

Step 3: Find the \( y \)-Intercepts of \( f(x) \)

The \( y \)-intercept occurs where \( x = 0 \). Substitute \( x = 0 \) into \( f(x) \): \[ f(0) = \frac{1}{0^2 - 3 \times 0 - 18} = \frac{1}{-18} = -\frac{1}{18} \]

Thus, the \( y \)-intercept is at \( y = -\frac{1}{18} \).

Final Answer

  1. The domain is all real \( x \), except \( x = 6, -3 \).
  2. There are no \( x \)-intercepts.
  3. The \( y \)-intercept is at \( y = -\frac{1}{18} \).

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -1, "ymax": 1}, "commands": ["y = 1/(x**2 - 3*x - 18)"], "latex_expressions": ["$y = \\frac{1}{x^2 - 3x - 18}$"]}

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Multiply and simplify. [ (x^2-7 x-18)/(2 x^2-162) cdot (x^2+18 x+81)/(2 x^2+22 x+36) ]
failedAnswered
Which pair of element and most common ionic charge is correct? Na / 1- C/6+ F/1+ Ba / 2+
failedAnswered
Universidad del Alba 2.- Encuentre las corrintes I1, I2 y I3 (20 Puntos)
failedAnswered
How are strategic plans and tactical plans different?
failedAnswered
Which term refers to the diffusion of water through a semipermeable membrane?