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This is the second of our many quizzes on Parent functions. Click on this to access more such competitive quizzes on Algebra.

Parent functions Quiz 2

mathematics

 Rama wants to check which of this is not a parent function? Help her in doing so

 A parent function is the simplest function that still satisfies the definition of a certain type of function.

A parent function is defined as the simplest function of a family of functions that preserves the definition (or shape) of the entire family. The basic parent functions by definition are linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent.

If a computer algorithm works such that the parent function denoted by the absolute positive value of any input is converted to shift its graph by 7 units down. What will be the new output if the standard graph is as shown? <img src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/70fc2405-0e68-4e9a-bf69-ad1a260a03748121758280029795145.png"/>

 When it is translated to 7 units down, the graph will shift towards the negative y-axis thereby getting a change in value.

Since a mod value is used, the said equation will be $f(x)=|x|$ With x as the independent variable. When it is translated to 7 units in the down, the graph will shift towards the negative y-axis thereby getting a change in value as $f(x)=|x|-7$

 An engineer wants to design a system such that it follows the rules of parent function $-{{x}^{2}}+1$ . What is the range and domain the engineer should consider for the system?

 The domain of a function is the complete set of possible values of the independent variable. The range of the function is all the values that can be taken by y according to the properties of this parent function

The graph of the said function is given as <img src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/47cf5ff3-0e30-4e2a-926b-0fcf79c5371d6406966653627729734.png"/> The domain of a function is the complete set of possible values of the independent variable The domain of the function is all the values that can be taken by x according to the properties of this parent function as x can accept all the possible values $domain=\{x:x\in R\}$ The range of a function is the complete set of all possible resulting values of the dependent variable The range of the function is all the values that can be taken by y according to the properties of this parent function. The least possible value this function can take is 1 $Range=\{y:y\le 1\}$ And the value is translated, from the standard parent function to the positive direction of the x axis as concluded by the properties of parent function

 A parent function given as the square root of the value is mirrored by the x axis and then shifted to the left by 2 units. What is the new equation obtained? 

 By the properties of parent function, if the function is inverted on the X axis, the function takes a negative value. 

We know, the square root of any value is expressed by the function $f(x)=\sqrt{x}$ By the properties of parent function, if the function is inverted on the X axis, the function takes a negative value. So the function will be represented as $f(x)=-\sqrt{x}$ If the function is shifted to the left by two units, by standard convention this means that the function is shifted to 2 units in the direction of the negative x axis. So 2 units are added to the function by the rules of transformation of the parent function. $f(x)=-\sqrt{x+2}$

 You have two functions $j(x)=\sqrt{x}$ and $k(x)=j(x+2)$ .Both functions tend to the general properties of Parent functions. What is the value of $k(x)$ in terms of x

 $k(x)$  is in terms of $j(x)$ since the two functions follow the general rules of parent functions therefore the value of  $j(x)$ can be substituted in  $k(x)$ to get the function $k(x)$ in terms of x

Given, $j(x)=\sqrt{x}$ and $k(x)=j(x+2)$ Here $k(x)$ is in terms of $j(x)$ since the two functions follow the general rules of parent functions therefore the value of $j(x)$ can be substituted in $k(x)$ to get the function in terms of x Substituting the value $k(x)=\sqrt{x+2}$