Question

Which answer choice best provides the critical information regarding the following rational function:

$$f(x) = \frac{x^2 + x - 6}{x^2 - x - 2} \div (x + 3)$$

Accepted Answer

Domain: $$x 
e -1$$, $$x 
e -3$$, $$x 
e 2$$   
Range: $$y 
e -\frac{1}{2}$$, $$y 
e \frac{1}{3}$$, $$y 
e 0$$   
Horizontal Asymptote: $$y = 0$$   
Vertical Asymptote: $$x = -1$$   
*y*-intercept: $$(0, 1)$$
End Behavior: $$f(x)$$ approaches negative infinity as *x* approaches $$-1$$ from the left. $$f(x)$$ approaches positive infinity as *x* approaches $$-1$$ from the right.

Answer

Domain: $$x 
e -1$$, $$x 
e -3$$, $$x 
e 2$$   
Range: $$y 
e \frac{1}{2}$$, $$y 
e \frac{1}{3}$$, $$y 
e 0$$   
Horizontal Asymptote: $$y = 0$$   
Vertical Asymptote: $$x = -1$$   
*y*-intercept: $$(0, 1)$$   
End Behavior: $$f(x)$$ approaches positive infinity as *x* approaches $$-1$$ from the left. $$f(x)$$ approaches positive infinity as *x* approaches $$-1$$ from the right.

Answer

Domain: $$x 
e -1$$, $$x 
e -3$$, $$x 
e 2$$   
Range: $$y 
e -\frac{1}{2}$$, $$y 
e \frac{1}{3}$$, $$y 
e 0$$   
Horizontal Asymptote: $$y = 0$$   
Vertical Asymptote: $$x = -1$$, $$x = -3$$, $$x = 2$$   
*y*-intercept: $$(0, 1)$$
End Behavior: $$f(x)$$ approaches negative infinity as *x* approaches $$-1$$ from the left. $$f(x)$$ approaches positive infinity as *x* approaches $$-1$$ from the right.

Answer

Domain: $$x 
e 1$$, $$x 
e -3$$, $$x 
e 2$$   
Range: $$y 
e -\frac{1}{2}$$, $$y 
e \frac{1}{3}$$, $$y 
e 0$$   
Horizontal Asymptote: $$y = 0$$   
Vertical Asymptote: $$x = 1$$    
*y*-intercept: $$(0, 1)$$   
End Behavior: $$f(x)$$ approaches positive infinity as *x* approaches $$-1$$ from the left. $$f(x)$$ approaches negative infinity as *x* approaches $$-1$$ from the right.

Question 11 - Next Generation Advanced Algebra and Functions Practice Test for the ACCUPLACER Test