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Hi! I don’t know how to do this, can somebody help?

Hi! I don’t know how to do this, can somebody help?-example-1

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Given:

The function are,


g(x)=6x^2-5

and


f(x)=x^2

Step-by-step explanation:

The function g(x) i a quadratic function and quadratic function is defined for all values of x. So domain of function f(x) is all real numbers.

The x-coordinate vertex of parabola ax^2 + bx + c = 0 is,


-(b)/(2a)

Fo the given quadratic equation a = 6, b = 0 and c = -5. So x-coordinate of vertex is,


-(0)/(2\cdot6)=0

Determine the y-coordinate of vertex.


\begin{gathered} g(0)=6\cdot(0)^2-5 \\ =-5 \end{gathered}

So minimum value of function is -5.

So range of function g(x) is,


\lbrack-5,\infty)

Domain and range in interval notation:

Domain:


(-\infty,\infty)

Range:


\lbrack-5,\infty)

Domain and range in set notation:

Domain:


\mleft\lbrace x|x\in\mathfrak{\Re }\mright\rbrace

Range:


\mleft\lbrace y|y\ge-5\mright\rbrace

Domain and range in inequality notation:

Domain:


-\inftyRange:[tex]-5\leq y<\infty

On compare the function g(x) with f(x), it can be observed that value of factor a is 6, which means function stretch vertically by a factor of 6.

The value of k is -5, means function translated down by 5 units.

Answer:

When compared to f(x), g(x) is stretched verticaly by a factor of 6, and translated down 5 units.

User LucyViolet
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