math 148

Daniel Kevins

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Sketch the graph of the given function. Use technology to approximate the intercepts, coordinates of extrema, and points of inflection to one decimal place. Check your sketch using technology. HINT [See Example 1.]

g(t) = 

1
4

t4 − 

2
3

t3 + 

1
2

t2

 
Correct: Your answer is correct.

(a) Indicate the t– and y-intercepts. (If an answer does not exist, enter DNE.)

t-intercept    
(t, y) =
leftparen1

  

rightparen1
y-intercept    
(t, y) =
leftparen1

  

rightparen1

(b) Indicate any extrema. (If an answer does not exist, enter DNE.)

    Correct: Your answer is correct.     
(t, y) =
leftparen1

  

rightparen1

(c) Indicate any points of inflection. (Order your answers from smallest to largest t. If an answer does not exist, enter DNE.)

(t, y) =
leftparen1

  

rightparen1
(t, y) =
leftparen1

  

rightparen1

(d) Indicate the behavior near points where the function is not defined.

y → +∞ as t → 0

y → 0 as t → 0

    

y → +∞ as t → 1

y → −∞ as t → ±1

Correct: Your answer is correct.

(e) Indicate the behavior at infinity.

y → +∞ as t → ±∞

y → −∞ as t → −∞; y → +∞ as t → +∞

    

y → −∞ as t → ±∞

y → +∞ as t → −∞; y → −∞ as t → +∞

Correct: Your answer is correct.

Need Help? Read It Practice It Chat About It

 

 
Correct: Your answer is correct.

(a) Indicate the x– and y-intercepts. (If an answer does not exist, enter DNE.)

x-intercept    
(x, y) =
leftparen1

  

rightparen1
y-intercept    
(x, y) =
leftparen1

  

rightparen1

(b) Indicate any extrema. (Order your answers from smallest to largest x. If an answer does not exist, enter DNE.)

    Correct: Your answer is correct.     
(x, y) =
leftparen1

  

rightparen1
    Correct: Your answer is correct.     
(x, y) =
leftparen1

  

rightparen1

(c) Indicate any points of inflection. (If an answer does not exist, enter DNE.)

(x, y) = 

leftparen1

  

rightparen1

(d) Indicate the behavior near points where the function is not defined.

y → +∞ as x → 0

y → 0 as x → 0

    

y → −∞ as x → 0

y → +∞ as x → 1

Correct: Your answer is correct.

(e) Indicate the behavior at infinity.

y → +∞ as x → −∞; y → −∞ as x →+∞

y → −∞ as x → ±∞

    

y → 1 as x → ±∞

y → +∞ as x → ±∞

y → −∞ as x → −∞; y → +∞ as x →+∞

Correct: Your answer is correct.

Need Help? Read It Practice It Chat About It

 

 
Correct: Your answer is correct.

(a) Indicate the x– and y-intercepts. (If an answer does not exist, enter DNE.)

x-intercept    
(x, y) =
leftparen1

  

rightparen1
y-intercept    
(x, y) =
leftparen1

  

rightparen1

(b) Indicate any extrema. (Order your answers from smallest to largest x. If an answer does not exist, enter DNE.)

    Correct: Your answer is correct.     
(x, y) =
leftparen1

  

rightparen1
    Correct: Your answer is correct.     
(x, y) =
leftparen1

  

rightparen1

(c) Indicate any points of inflection. (If an answer does not exist, enter DNE.)

(x, y) = 

leftparen1

  

rightparen1

(d) Indicate the behavior near points where the function is not defined.

y → −∞ as x → 0

y → 0 as x → ±1

    

y → +∞ as x → −2

y → +∞ as x → −1

Correct: Your answer is correct.

(e) Indicate the behavior at infinity.

y → +∞ as x → ±∞

y → −∞ as x → −∞; y → +∞ as x → +∞

    

y → −∞ as x → ±∞

y → +∞ as x → −∞; y → −∞ as x → +∞

Correct: Your answer is correct.

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Daniel Kevins

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