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kolbaska11 [484]
3 years ago
7

The function h(x)= 12x^8+49 is an even function. Which transformation of h(x) would result in a function that is neither even no

r odd?
Mathematics
1 answer:
egoroff_w [7]3 years ago
6 0

Answer:

A translation (9 units) to the left will result in a function that is neither even nor odd

Step-by-step explanation:

With horizontal translation to the left, we have;

h(x) = 12(x - 9)⁸ + 49

Which gives;

h(x) = 12(x - 9)⁸ + 49 = 12(x⁸ - 72x⁷ + 2268x⁶ - 40824x⁵ + 459270x⁴ -3306744x³ + 14880348x² - 38263752x + 43046721) + 49

For x = 1, we get;

h(x) = 201326641

When we replace x by -x, we get;

h(x) = 12(-x - 9)⁸ + 49 = 12(x⁸ + 72x⁷ + 2268x⁶ + 40824x⁵ + 459270x⁴ + 3306744x³ + 14880348x² + 38263752x + 43046721) + 49

For x = 1, we get;

h(x) = 1200000049

Therefore a translation 9 units to the left will result in a function that is neither even nor odd.

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Answer:

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Hi there!

<u>What we need to know:</u>

  • Linear equations are typically organized in slope-intercept form: y=mx+b where <em>m</em> is the slope and <em>b</em> is the y-intercept
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<u>Determine the slope (</u><em><u>m</u></em><u>):</u>

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The slope of the given line is \displaystyle-\frac{4}{3}, since it is in the place of <em>m</em> in y=mx+b. Because parallel lines always have the same slope, the slope of a parallel line would also be \displaystyle-\frac{4}{3}. Plug this into y=mx+b:

y=\displaystyle-\frac{4}{3}x+b

<u>Determine the y-intercept (</u><em><u>b</u></em><u>):</u>

y=\displaystyle-\frac{4}{3}x+b

To find the y-intercept, plug in the given point (6,14) and solve for <em>b</em>:

14=\displaystyle-\frac{4}{3}(6)+b\\\\14=-8+b\\b=22

Therefore, the y-intercept of the line is 22. Plug this back into y=\displaystyle-\frac{4}{3}x+b:

y=\displaystyle-\frac{4}{3}x+22

I hope this helps!

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