Algebra Flashcards
What does f(x+2) mean?
Translate left 2
What does f(x)+2 mean?
Translate up 2
What does -f(x) mean?
Reflect in the X axis.
What does f(-x) mean?
Reflect in the Y axis.
What does 2f(x) mean?
Vertical stretch by a factor of 2
Multiply every Y value by 2
What does f(2x) mean?
Horizontal stretch by a factor of one half.
Multiply all the x values by 0.5
What does a Y=cos X graph look like.
It repeats it’s self every 360 on the X axis.
At 0 on the X axis it is at 1 on the Y. At 90 this falls to 0 and it is at its lowest at 180 on the X axis at -1. It will then go up through (270,0) and reach 1 on the Y axis at 360.
What does a graph of y=sin x look like ?
It repeats its self 360 on the X axis. It starts at (0,0) and reaches its highest point is at (90,1). From here it will fall to (180,0) and continue untill it reaches (270,-1). It will then go up from here where it will reach 0 at 360. Then it will repeat.
What does the curve of 2sin x look like?
Like a curve to sin x but the amplitude is twice as big. It is higher and lower.
What does a curve of cos 3x look like?
It changes the wavelength to make it shorter. The curve will repeat its self three times over the period of 360, not just once
What does a curve of 2 cos x look like?
It doubles the amplitude of a cos graph.
What does a curve of sin 2x look like?
It is a sin graph that repeats itself twice over the period of 360.
What does a graph of cos x-1 look like?
What would it look like if it was + 1?
It is an ordinary cos graph that has been lowed by one. It will start to go down at the origin.
It would have gone up one if it was a plus.
Same for sin graphs.
What does a cos(x-180) or a sin(x+90) look like?
The sin graph would have been moved 90 to the left, the other 180 to the right.
What are the coordinates of the point where the line y=2x+5 cuts into the Y axis?
Well at this point, the X value will be 0. Two times 0 is still 0 but you add five so your final answer should be (0,5)
What are the coordinates of the point where the line y=2x+5 cuts into the X axis?
When it touches the X axis, the Y value will be 0 so 0=2x+5
-5=2x
x=-2.5
The final answer is (-2.5,0)
If you have to divide 1 by a fraction, what do you do?
You find the reciprocal of the fraction by swamping the two number in the fraction around.
If you did one divided by 5/7 is would become 7/5
What is the simple way of factoring x^2 +3x -28 ?
Find two numbers that add to get 3 and multiply to get minus 28
Here is 7 and -4
(X-4) (x+7)
Solve the quadratic x^2 -5x-36=0 by factoring.
4 and -9 add to give -5 and multiply to give -36.
(X+5x) (x-9)
X is 9 is minus 4
Factorise x^2 +5x
X(x+5)
How do you complete the square?
Half the coefficient of x and subtract the square of this from the constant.
If you have to draw a graph of x^2 + y^2 =25 what do you do?
Draw a circle around the origin with a radius of 5 (the square root of 25)
How do you simplify a surd ?
Find the largest square number that goes into it and the other number it multiples by. Undo the surfs after this.
What does a quadratic graph look like?
Any graph with a squared in it.
Like an un-happy mouth. It goes up from one side, gets flat at the top and down on the other side.
If you had the fraction 4x/76x, how could you simplify it?
Remove the Xs and it becomes 4/76
If you have a quadratic simulations equation to solve and are asked about the relationships the two equations would have on a graph, what would you answer?
If you get an equation with x^2 + y^2=5 it will be a circle. The other will probably be a line.
If you have four different answers, the line will intersect the circle. If you have two values, the line is a tangent to the circle, if it can’t be solved, the circle and line don’t meet.
What is 3y^2-3y factories?
3y (y-1)
What is 10x ÷ 2x?
5
