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# definition of parent functions

Question:im in algebra 2 and i have a project. i have to draw a picture made of functions. i have to include all 6 parents functions. i know there is linear quadratic cubic root and square root. What are the other 2? please help!!! THANKS!!

Answers:probably the absolute value (which looks like a V) and the cube function (y = x^3)

Question:1.Linear Parent 2.Absolute value 3.Quadratic 4.Square root 5.Cubic 6.Rational/Reciprocal Tell At least 4 characteristics about each. For example: What is the general shape? How many x intercepts does it have? Where are these equations seen? What is the domain and range? Is the function even/odd/neither? Are there any interesting facts about this parent function?

Answers:You could have just added this in to the additional details.... Linear: f(x)=x this is a straight line (ie linear) it has on x intercept (0) these equations are found by graphic a constant speed on a time/distance graph. D is all real numbers and R is all real. Function is odd (ie symmetrical from (0,0) Absolute value: f(x)= |x| The general shape is a V, it as one x intercept at 0 (the parent function does but it can have up to two), the are seen when you are only looking for positive y answers (ie distance)..... D is any real numbers and R is anything greater than 0, the function is even (symmetrical from the y axis) Quadratic: f(x)=x^2 General shape is a U, parent only has one x intercept but can have 2, D is any real number and R is anything greater than 0.... Even Square Root: f(x)= sqrt(x) GS- Steep closer to the origin but it flattens out (relative to the x axis) as you get farther away. One x intercept at 0. Domain is anything greater than 0 and range is any positive real number. Neither odd nor even Cubic: f(x)=x^3 GS- Looks like an S that has been turned sideways and stretched (http://www.google.com/imgres?imgurl=http://library.thinkquest.org/2647/media/oddxxx.gif&imgrefurl=http://library.thinkquest.org/2647/algebra/ftevenodd.htm&usg=__BxjG9VWZU593Jp7jRgtxmGIqWoc=&h=317&w=365&sz=3&hl=en&start=0&sig2=c49qej0i_HjEhrwj6KVCVg&zoom=1&tbnid=fQob5GWIX1BdNM:&tbnh=126&tbnw=144&ei=xz6ZTPK4C4P88AaW89DvDw&prev=/images%3Fq%3Df(x)%253Dx%255E3%26um%3D1%26hl%3Den%26safe%3Doff%26biw%3D1440%26bih%3D673%26tbs%3Disch:1&um=1&itbs=1&iact=hc&vpx=128&vpy=74&dur=342&hovh=126&hovw=145&tx=90&ty=95&oei=xz6ZTPK4C4P88AaW89DvDw&esq=1&page=1&ndsp=31&ved=1t:429,r:0,s:0) One x intercept at 0,0 Domain is any real number and range is any real number... Function is odd Reciprocal: f(x)=1/x GS-http://www.mathsrevision.net/gcse/functions.php No x intercepts Domain is any real number besides 0 and range is any real number besides 0.... I hope THIS answers your question....

Question:For each type of parent function, we have to fill in certain information based on the the info they give us already. 1. Rational function. It says that they domain is all real numbers except 2, and the range is all real numbers except 1. I have to find the description of transformation, write the new equation, and graph it. 2. Square root function. The description of the transformation is reflected over the y-axis, and is shifted 3 units left. I have to find the domain and range, the new equation, and plot the graph. 3. Quadratic function. The description of the transformation is reflected over the y-axis, the graph is stretched by a factor of 4, and shifted 2 units up. I have to find the domain and range, write the new equation, and plot the graph. Please help me and please explain the process! Thanks so much!!!