math 148
johnne1Sketch 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) =
t4 −
t3 +
t2
| 1 |
| 4 |
| 2 |
| 3 |
| 1 |
| 2 |
 |
(a) Indicate the t- and y-intercepts. (If an answer does not exist, enter DNE.)
(b) Indicate any extrema. (If an answer does not exist, enter DNE.)
(c) Indicate any points of inflection. (Order your answers from smallest to largest t. If an answer does not exist, enter DNE.)
(d) Indicate the behavior near points where the function is not defined.
(e) Indicate the behavior at infinity.
| t-intercept | (t, y) = |
| ||
| y-intercept | (t, y) = |
|
(b) Indicate any extrema. (If an answer does not exist, enter DNE.)
| | (t, y) =
|
(c) Indicate any points of inflection. (Order your answers from smallest to largest t. If an answer does not exist, enter DNE.)
(t, y) = |
| ||
(t, y) = |
|
(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
(e) Indicate the behavior at infinity.
y → +∞ as t → ±∞
y → −∞ as t → −∞; y → +∞ as t → +∞
y → −∞ as t → ±∞
y → +∞ as t → −∞; y → −∞ as t → +∞
(a) Indicate the x- and y-intercepts. (If an answer does not exist, enter DNE.)
(b) Indicate any extrema. (Order your answers from smallest to largest x. If an answer does not exist, enter DNE.)
(c) Indicate any points of inflection. (If an answer does not exist, enter DNE.)
(d) Indicate the behavior near points where the function is not defined.
(e) Indicate the behavior at infinity.
| x-intercept | (x, y) = |
| ||
| y-intercept | (x, y) = |
|
(b) Indicate any extrema. (Order your answers from smallest to largest x. If an answer does not exist, enter DNE.)
| | (x, y) =
| ||
| | (x, y) =
|
(c) Indicate any points of inflection. (If an answer does not exist, enter DNE.)
(x, y) =
 |
 |
(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
(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 →+∞
(a) Indicate the x- and y-intercepts. (If an answer does not exist, enter DNE.)
(b) Indicate any extrema. (Order your answers from smallest to largest x. If an answer does not exist, enter DNE.)
(c) Indicate any points of inflection. (If an answer does not exist, enter DNE.)
(d) Indicate the behavior near points where the function is not defined.
(e) Indicate the behavior at infinity.
| x-intercept | (x, y) = |
| ||
| y-intercept | (x, y) = |
|
(b) Indicate any extrema. (Order your answers from smallest to largest x. If an answer does not exist, enter DNE.)
| | (x, y) = |
| ||
| | (x, y) = |
|
(c) Indicate any points of inflection. (If an answer does not exist, enter DNE.)
(x, y) =
|
|
(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
(e) Indicate the behavior at infinity.
y → +∞ as x → ±∞
y → −∞ as x → −∞; y → +∞ as x → +∞
y → −∞ as x → ±∞
y → +∞ as x → −∞; y → −∞ as x → +∞
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