Exponential Functions

Question 1

what is the formula for an Exponential function

Answer 1

y = a . b ^x+p + q

Question 2

what does p effect

Answer 2

As with our previous functions, replacing x with x + p shifts our function to the left or the right by an amount of p.

P is the Horizontal Shift

if p is positive the graph is shifted to the left by p units

if p is negative the graph is shifted to the right by p units

Question 3

what does q effect

Answer 3

q is is avertical shift.It also affects theasymptote(horizontal) of the line y = q

if q is positive the graph is shifted upwards by q units

if q is negative the graph is shifted downwards by q units

Question 4

what does a effect

Answer 4

The value of a affects theshapeof the graph and itspositionrelative to the horizontal asymptote.We can think of a as stretching or squishing the graph, or even rotating it over the x - axis

if a is positive the graph is increasing in size

if a is negative the graph is decreasing in size

• if a is positive the graph lies above the horizontal asymptote.
• if a is negative the graph lies below the horizontal asymptote.

Question 5

what do we need to have before sketching a graph

Answer 5

• Shape
• Intercepts
• Asymptote
• Domain and range