If the parent function is \root(3)(x), describe the translation of the function y=\root(3)(x+4)-3

Mathematics

1 answer:

xeze [42]2 years ago

7 0

The parent function moves 4 units right and 3 units down. This is a translation by the vector.

According to the question,

Transformation $\sqrt[3]{x}$ maps onto $\sqrt[3]{x+4} -3$ . Take f(x) = $\sqrt[3]{x}$ and f(x+4)= $\sqrt[3]{x+4}$ .

f(x) = $\sqrt[3]{x}$

f(x+4)= $\sqrt[3]{x+4}$

f(x+4) - 3= $\sqrt[3]{x+4}$ - 3

Analyze the function to see the translations. f(x-4) corresponds to a horizontal translation 4 units in the positive 'x' direction. f(x)-3 corresponds to a vertical translation 3 units in the negative 'y' direction.

Hence, the parent function moves 4 units right and 3 units down. This is a translation by the vector.

Learn more about parent function here

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How to solve (8.76 x 109)(6.52 x 10-3)/13.27 x 105?

SVEN [57.7K]

Use PEMDAS:
P = parenthesis
E = exponents
M = multiplication
D = division
A = addition
S = subtraction

First, start with the parenthesis:
(8.76 * 109)(6.52 * 10 - 3) / 13.27 * 105
(954.84)*(62.2) / 13.27 * 105

Then do ALL multiplication:
59,391.048 / 1,393.35

Now do all division:
42.62

So, your final answer is 42.62

6 0

3 years ago

Write the equation in slope-intercept form through the point (-5, 3) and is perpendicular to the line y = 2x - 3 and graph

xxTIMURxx [149]

Slope intercept form: y = mx + b

When a line is perpendicular to another line, its slope is the negative reciprocal to that slope.

From this information, we already know that the slope of our new line is -1/2, because -1/2 is the negative reciprocal to 2 (which is the slope of the original line).

y = -1/2x + b

Because the point (-5,3) is given, we can simply plug the x and y coordinates into our incomplete equation.

3 = -1/2(-5) + b

3=2.5 + b

b = 0.5

ANSWER: y = -1/2x + 0.5

THE GRAPH IS LINKED; RED LINE IS y=2x-3 AND BLUE LINE IS y=-1/2x + 0.5