Math / Algebra

QuestionEvaluate the function at the specified points. $f(x, y)=y+x y^{2},(-2,4),(-3,-2),(-5,4)$
At $(-2,4)$ : $\square$ At $(-3,-2)$ : $\square$ At $(-5,4)$ : $\square$ Submit answer Next item

Studdy Solution

STEP 1

1. We are given the function $f(x, y) = y + xy^2$ .
2. We need to evaluate this function at three specified points: $(-2, 4)$ , $(-3, -2)$ , and $(-5, 4)$ .

STEP 2

1. Substitute the first point $(-2, 4)$ into the function and evaluate.
2. Substitute the second point $(-3, -2)$ into the function and evaluate.
3. Substitute the third point $(-5, 4)$ into the function and evaluate.

STEP 3

Substitute $x = -2$ and $y = 4$ into the function $f(x, y) = y + xy^2$ :
$f(-2, 4) = 4 + (-2)(4)^2$

STEP 4

Simplify the expression:
$f(-2, 4) = 4 + (-2)(16)$ $f(-2, 4) = 4 - 32$ $f(-2, 4) = -28$

STEP 5

Substitute $x = -3$ and $y = -2$ into the function:
$f(-3, -2) = -2 + (-3)(-2)^2$

STEP 6

Simplify the expression:
$f(-3, -2) = -2 + (-3)(4)$ $f(-3, -2) = -2 - 12$ $f(-3, -2) = -14$

STEP 7

Substitute $x = -5$ and $y = 4$ into the function:
$f(-5, 4) = 4 + (-5)(4)^2$

STEP 8

Simplify the expression:
$f(-5, 4) = 4 + (-5)(16)$ $f(-5, 4) = 4 - 80$ $f(-5, 4) = -76$
The evaluated function values are:
At $(-2, 4)$ : $-28$
At $(-3, -2)$ : $-14$
At $(-5, 4)$ : $-76$

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QuestionEvaluate the function at the specified points. $f(x, y)=y+x y^{2},(-2,4),(-3,-2),(-5,4)$
At $(-2,4)$ : $\square$ At $(-3,-2)$ : $\square$ At $(-5,4)$ : $\square$ Submit answer Next item

Studdy Solution

STEP 1

1. We are given the function $f(x, y) = y + xy^2$ .
2. We need to evaluate this function at three specified points: $(-2, 4)$ , $(-3, -2)$ , and $(-5, 4)$ .

STEP 2

1. Substitute the first point $(-2, 4)$ into the function and evaluate.
2. Substitute the second point $(-3, -2)$ into the function and evaluate.
3. Substitute the third point $(-5, 4)$ into the function and evaluate.

STEP 3

Substitute $x = -2$ and $y = 4$ into the function $f(x, y) = y + xy^2$ :
$f(-2, 4) = 4 + (-2)(4)^2$

STEP 4

Simplify the expression:
$f(-2, 4) = 4 + (-2)(16)$ $f(-2, 4) = 4 - 32$ $f(-2, 4) = -28$

STEP 5

Substitute $x = -3$ and $y = -2$ into the function:
$f(-3, -2) = -2 + (-3)(-2)^2$

STEP 6

Simplify the expression:
$f(-3, -2) = -2 + (-3)(4)$ $f(-3, -2) = -2 - 12$ $f(-3, -2) = -14$

STEP 7

Substitute $x = -5$ and $y = 4$ into the function:
$f(-5, 4) = 4 + (-5)(4)^2$

STEP 8

Simplify the expression:
$f(-5, 4) = 4 + (-5)(16)$ $f(-5, 4) = 4 - 80$ $f(-5, 4) = -76$
The evaluated function values are:
At $(-2, 4)$ : $-28$
At $(-3, -2)$ : $-14$
At $(-5, 4)$ : $-76$

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Studdy Solution

STEP 1

1. We are given the function f(x,y)=y+xy2 f(x, y) = y + xy^2 f(x,y)=y+xy2.2. We need to evaluate this function at three specified points: (−2,4)(-2, 4)(−2,4), (−3,−2)(-3, -2)(−3,−2), and (−5,4)(-5, 4)(−5,4).

STEP 2

1. Substitute the first point (−2,4)(-2, 4)(−2,4) into the function and evaluate.2. Substitute the second point (−3,−2)(-3, -2)(−3,−2) into the function and evaluate.3. Substitute the third point (−5,4)(-5, 4)(−5,4) into the function and evaluate.

STEP 3

Substitute x=−2 x = -2 x=−2 and y=4 y = 4 y=4 into the function f(x,y)=y+xy2 f(x, y) = y + xy^2 f(x,y)=y+xy2:f(−2,4)=4+(−2)(4)2 f(-2, 4) = 4 + (-2)(4)^2 f(−2,4)=4+(−2)(4)2

STEP 4

Simplify the expression:f(−2,4)=4+(−2)(16) f(-2, 4) = 4 + (-2)(16) f(−2,4)=4+(−2)(16) f(−2,4)=4−32 f(-2, 4) = 4 - 32 f(−2,4)=4−32 f(−2,4)=−28 f(-2, 4) = -28 f(−2,4)=−28

STEP 5

Substitute x=−3 x = -3 x=−3 and y=−2 y = -2 y=−2 into the function:f(−3,−2)=−2+(−3)(−2)2 f(-3, -2) = -2 + (-3)(-2)^2 f(−3,−2)=−2+(−3)(−2)2

STEP 6

Simplify the expression:f(−3,−2)=−2+(−3)(4) f(-3, -2) = -2 + (-3)(4) f(−3,−2)=−2+(−3)(4) f(−3,−2)=−2−12 f(-3, -2) = -2 - 12 f(−3,−2)=−2−12 f(−3,−2)=−14 f(-3, -2) = -14 f(−3,−2)=−14

STEP 7

Substitute x=−5 x = -5 x=−5 and y=4 y = 4 y=4 into the function:f(−5,4)=4+(−5)(4)2 f(-5, 4) = 4 + (-5)(4)^2 f(−5,4)=4+(−5)(4)2

STEP 8

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1. We are given the function $f(x, y) = y + xy^2$ .
2. We need to evaluate this function at three specified points: $(-2, 4)$ , $(-3, -2)$ , and $(-5, 4)$ .

1. Substitute the first point $(-2, 4)$ into the function and evaluate.
2. Substitute the second point $(-3, -2)$ into the function and evaluate.
3. Substitute the third point $(-5, 4)$ into the function and evaluate.

Substitute $x = -2$ and $y = 4$ into the function $f(x, y) = y + xy^2$ :
$f(-2, 4) = 4 + (-2)(4)^2$

Simplify the expression:
$f(-2, 4) = 4 + (-2)(16)$ $f(-2, 4) = 4 - 32$ $f(-2, 4) = -28$

Substitute $x = -3$ and $y = -2$ into the function:
$f(-3, -2) = -2 + (-3)(-2)^2$

Simplify the expression:
$f(-3, -2) = -2 + (-3)(4)$ $f(-3, -2) = -2 - 12$ $f(-3, -2) = -14$

Substitute $x = -5$ and $y = 4$ into the function:
$f(-5, 4) = 4 + (-5)(4)^2$