PRE CALCULUS
1 answer:
Start with the parent function f(x) = x³
Notice the function f(x) = (x - 4)³ that a value '4' is subtracted from 'x' ⇒ This means the function f(x) is translated four units to the right.
Then the function f(x) = ¹/₂ (x - 4)³, the function (x - 4)³ is halved vertically ⇒ Half the y-coordinate
Then the function f(x) = ¹/₂ (x - 4)³ + 5 that a value '5' is added to ¹/₂ (x - 4)³ ⇒ This means the function f(x) is translated five units up
So the order of transformation that is happening to f(x) = x³ is translation four units to the right, half the y-coordinate, then translate 5 units up.
Notice the function f(x) = (x - 4)³ that a value '4' is subtracted from 'x' ⇒ This means the function f(x) is translated four units to the right.
Then the function f(x) = ¹/₂ (x - 4)³, the function (x - 4)³ is halved vertically ⇒ Half the y-coordinate
Then the function f(x) = ¹/₂ (x - 4)³ + 5 that a value '5' is added to ¹/₂ (x - 4)³ ⇒ This means the function f(x) is translated five units up
So the order of transformation that is happening to f(x) = x³ is translation four units to the right, half the y-coordinate, then translate 5 units up.
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Let us say, the number is "a"
one less than "a" is ... well a - 1
2/5 of that will be... well, 2/5 * ( a - 1)
one more than "a" is... well a + 1
3/5 of that is.. hmmm 3/5 * (a + 1)
now, we're told that, the first expression is "less than" the second one, thus
solve for "a", or make it "x" if you wish, same thing anyway
one less than "a" is ... well a - 1
2/5 of that will be... well, 2/5 * ( a - 1)
one more than "a" is... well a + 1
3/5 of that is.. hmmm 3/5 * (a + 1)
now, we're told that, the first expression is "less than" the second one, thus
solve for "a", or make it "x" if you wish, same thing anyway