3.) Graphs

Question 1

How do find a gradient of a perpendicular line to the original line?

Answer 1

Question 2

Y = cos(X) graph

Answer 2

• Fully repeats itself every 360°
• Y = 0 at -90°, 90°, 270° and at every 180° interval
• Y = 1 at 0°, 360° etc
• Y = -1 at -180°, 180° etc

Question 3

Y = sin(X) graph

Answer 3

• Fully repeats itself every 360°
• Y = 0 at -180°, 0°, 180°, 360° and at every 180° interval
• Y = 1 at -270°, 90° etc
• Y = -1 at -90°, 270° etc

Question 4

Y = tan(X) graph

Answer 4

• Fully repeats itself every 180°
• Y goes up to infinity every time you reach 90°, 270 (every 180° interval)
• Y = 0 at -180°, 0°, 180°, 360° and at every 180° interval

Question 5

How do you translate (or move) a graph along the Y axis?

Answer 5

• Y =f(X) + a
• Where the graph moves up/down by a (negative will move down, positive moves it up)

Question 6

How do you translate (or move) a graph along the Y axis?

Answer 6

• Y =f(X - a)
• A bit tricky at first, but the graph moves along the X axis in the direction of a
• I.e. Y =f(X - 4) moves a graph RIGHT by 4, not left as one might assume

Question 7

How do you reflect a graph along the Y or X axes?

Answer 7

• For reflecting in the Y axis: Y = f(-X)
• For reflecting in the X axis: Y = -f(X)
• A good way to visualise this is picturing the reflected y-intercept: the y-intercept would not move if the whole graph is reflected on the y-axis, but it will if the graph is reflected on the x-axis

Question 8

Answer 8

• They are symmetrical to either Y = X or Y = -X
• Y can never be zero in either, so the lines cannot ever touch the X axis

Question 9

What do Y = K^x graphs look like? (Y = 2^x and Y = 2^-x for example) And general rules for Y = K^x graphs

Answer 9

• Without a coefficient (f in f * K^x), the Y intercept will always be 1)
• When there is a coefficient, then the Y intercept is whatever the coefficient is
• K signals the general steepness of the graph

Question 10

How do you find the distance travelled in a velocity-time graph?

Answer 10

• It is the area under the graph

Question 11

How do you find the speed at a given point from a distance time graph?

Answer 11

• The gradient of the graph of that given point
• The steeper the gradient, the faster the speed
• A negative gradient signals the travelling object returning to the start/travelling in the opposite direction