State the domain of the function: $$g\left(x\right)\ =\ \sqrt[3]{x-3}\ -1$$

Domain: $$\left(-\infty,\ +\infty\right)$$

Domain: $$\left[3,\ \infty\right)$$

Domain: $$\left[-3,\ \infty\right)$$

State the range of the function: $$g\left(x\right)\ =\ \sqrt[3]{x-3}\ -1$$

Domain: $$\left(-\infty,\ +\infty\right)$$

Domain: $$\left[3,\ \infty\right)$$

Domain: $$\left[-3,\ \infty\right)$$

Let $$f\left(x\right)\ =\ \sqrt[]{x\ +\ 1.5}$$ and $$f^{-1}\ \left(x\right)\ =\ x^2\ -1.5$$ , state the domain of f(x). Hint, what number can you put into the radical to = 0?

domain: $$\left[-1.5,\ \infty\right)$$

domain: $$\left(-\infty,\ -1.5\right]\ U\ \left[1.5,\ \infty\right)$$

domain: $$\left(-\infty,\ 1.5\ U\ \left(1.5,\ \infty\right)\right)$$

domain: $$\left[1.5,\ \infty\right)$$

Let $$f\left(x\right)\ =\ \sqrt[]{x\ +\ 1.5}$$ and $$f^{-1}\ \left(x\right)\ =\ x^2\ -1.5$$ , state the domain of $$f^{-1}\left(x\right)$$ . Hint, the domain of $$f^{-1}\left(x\right)$$ is the range of f(x).

domain: $$\left[0,\ \infty\right)$$

domain: $$\left(-\infty,\ -1.5\right]\ U\ \left[1.5,\ \infty\right)$$

domain: $$\left(-\infty,\ 1.5\ U\ \left(1.5,\ \infty\right)\right)$$

domain: $$\left[1.5,\ \infty\right)$$

Find the point discontinuities, vertical asymptote, and horizontal asymptote of the following function:

P.D.: x = -5 V.A.: x = = 5 H.A.: y = 0

P.D.: none V.A.: x = = 5, -5 H.A.: y = 0

P.D.: x = 5 V.A.: x = = -5 H.A.: y = 0

P.D.: x = -5 V.A.: x = = 5 H.A.: none

Let $$f\left(x\right)\ =\ \frac{\left(2x^2\right)}{\left(9-x^2\right)}$$ . Identify the vertical asymptotes, point discontinuities, and horizontal asymptotes.

P.D.: x = none V.A.: x = 3, -3 H.A.: y = -2

P.D.: x = none V.A.: x = 3 (multiplicity) H.A.: y = -2

P.D.: x = -3 V.A.: x = 3 H.A.: y = -2

P.D.: x = none V.A.: x = -3 (multiplicity) H.A.: y = -2

Let $$f\left(x\right)\ =\ \frac{\left(2x^2\right)}{\left(9-x^2\right)}$$ . Identify the x and y intercept (if ay).

x-intercept: (0,0) y-intercept: (0,0)

x-intercept: (1,0) y-intercept: (0,1)

x-intercept: (1,0) y-intercept: (0,-1)

x-intercept: (0,1) y-intercept: (1,0)

Identify the following: 1. point discontinuities 2. vertical asymptotes 3. horizontal asymptotes 4. x-intercepts 5. y-intercepts

P.D.: x = -2 V.A.: x = -1 H.A.: y = 2 X-Int: x = -3, (-3,0) Y-Int: y = 6, (0,6)

P.D.: x = -2 V.A.: x = -1 H.A.: y = 2 X-Int: x = 3, (3,0) Y-Int: y = -6, (0,-6)

P.D.: x = 2 V.A.: x = 1 H.A.: y = -2 X-Int: x = -3, (-3,0) Y-Int: y = 6, (0,6)

P.D.: x = -2 V.A.: x = 1 H.A.: y = -2 X-Int: x = -3, (-3,0) Y-Int: y = 6, (0,6)

Pre-Calculus Test - Chapter 2: Radical, Polynomial, and Rational

Authored by Joseph Lloyd

Mathematics

12th Grade

CCSS covered

Used 2+ times

Pre-Calculus Test - Chapter 2: Radical, Polynomial, and Rational

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OPEN ENDED QUESTION

15 mins • 5 pts

Please attach your graph with labeled points. You may use a calculator for this to identify the transformation. Hint, there is no horizontal stretch or compress, along with no vertical stretch or compress.

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