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Find all intercepts for y = (x+5) * sqrt(4-x^4)?

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Find all intercepts for y = (x+5) * sqrt(4-x^4)?

asked Aug 24, 2015 in PRECALCULUS by anonymous

1 Answer

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Step 1:

The equation is image.

Domain :

The domain of a  function is the set of values of  for which the function is mathematically correct.

The function  under the square root should not be negative.

image.

Solve the inequality image.

is always greater than zero, hence .

Therefore, the domain of the function is image.

Range :

Range is the output values of the function.

The range of the function is image.

Step 2:

Find the - intercept by susbtituting in image.

or .

or image

or image

or image

is not in the domian of the function .

Therefore,the - intercepts are  image.

Step 3:

Find image- intercept by substituting image in image.

image

image

image

image.

image is the not in the range of the function.

Therefore the image- intercept is image.

Solution :

The -intercepts are image and image- intercept is image.

answered Aug 24, 2015 by lilly Expert

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