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### 30 Cards in this Set

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 if y=g(x) is a function, and p(x) is the graph of g(x) shifted up vertically by two units, what is p(x) in terms of g(x)? p(x)=g(x)+2 If y=u(x) is a function and h(x) is the graph of u(x) shifted left two and down 10, what is the formula for h(x) in terms of u(x)? h(x)=u(x+2)-10 If r(x) is a function, then r(x-c) denotes a horizontal shift of r(x) to the _______ and r(x+c) denotes a horizontal shift of r(x) to the _______ by how many units? right left c If a function is to be horizontally shifted and also vertically shifted does it matter which order you perform vertical and horizontal shifts? No, you can perform the shifts in any order. The order of operations does matter when you deal with compressions and stretches but not with shifts. If f is an even function than what is algebraically true about f? f(-x)=x How would you prove that y=(x^3) +5x is an odd function? Need to show that f(-x)=-f(x) Therefore f(-x)= (-x)^3 +5(-x) = -x^3 -5x and -f(x) = -1*((x^3) +5x) = -x^3-5x so f(-x)=-f(x) How would you show that y=x^2+2x-1 is an even function? show that f(-x)=f(x) f(-x)=(-x)^2 +2(-x) -1 = x^2 -2x -1 since this = f(x) the function is even If f is an odd function then it is symmetric with respect to the _______ and obeys which algebraic property? origin f(-x)=-f(x) If f is an even function then it is symmetric with respect to the _______ and obeys which algebraic property? y axis f(-x)=f(x) True or false, if a function is symmetric with respect to the origin, then flipping it over the y axis then over the x- axis will give you back the original function? true True or false If a function is even, you can flip it across the x axis and you will get the same function back false, you must flip it over the y-axis since even functions are symmetric with respect to the y-axis. If f is a function and k is a constant then how does y=kf(x) relate to the graph of y=f(x), if: 1. k>1 2. 01 2. 00 the parabola opens_________ downward upward if a<0 then the graph of the quadratic: is concave down or concave up? has a max or a min? what about if a>0? concave down, has a max concave up, has a max to change a quadratic equation from standard form to vertex form one must....... complete the square example: 2x^2 - 12x + 20 2[x^2-6x+10] 2[(x- ? )^2 + 10 -?] 2[(x-3)^2 + 10 -9] 2[(x-3)^2 +1] 2(x-3)^2 + 2 to change a quadratic equation from vertex form to standard form one must..... multiply out the squared term in the vertex form and simplify. example: y= 2(x-3)^2 -1 =2(x-3)(x-3)-1 = 2[x^2 -6x +9] -1 = 2x^2 -12x +18-1 = 2x^2 -12x +17 What are the steps to completing the square for a general function: y=ax^2 +bx +c 1. factor a out of the equation 2. take x and depending on the sign, add or subtract b/2. 3. Square the above term. 4. Subtract (b/2)^2 from the equation 5. simplify and multiply the a factor back into the equation True or false, one can always recognize a quadratic function by whether or not it has a 2 as the highest exponent. True, quadratic equations always take the form y=ax^2 +bx +c y=-f(x) is a reflection of f(x) across which axis? y=f(-x) is a reflection of f(x) across which axis? x-axis y-axis True or false, the graph of every quadratic equation is a parabola True