MCR3U - Exponential Functions Test Notes

MCR3U – Grade 11 Functions – Exponential Functions Test Notes Exponential Unit Study Notes Exponent Laws Exponent Laws Formula Multiplication (a^n)*(a^n) = a^(m+n) Division (a^n)/(a^m) = a^(n-m) Power (a^n)^m = a^(n*m) Negative A^-b = (1/a)^b Zero A^0 = 1 Power of a product (xy)^a = x^a*y^a Power of a quotient (x/y)^a = (x^a)/(y^a) Fractional Exponent A^(2/2) = 2 root (a^2) Basic Techniques -Take multiplying terms with negative exponents down or up in a fraction to remove negativity -Terms with the same base can have exponent’s added/subtracted/multiplied -When exponent variables are solved using the same base, the base can be eliminated, leaving youwith the exponent variable problems to solve. Exponential Functions -f(x) = ab^(x) -b : is the base of the exponent -if b > 0, then the function is increasing -if b < 0, then the function is decreasing -A is the initial value (y intercept) which also defines the asymptote Transformations of functions Vertical Stretch -a’s value dictates vertical stretch/compression -if a > 1, then the function is stretched vertically by the factor of a

-if 0 < a < 1, then the function is compressed by the factor of a -Values of y increases/decreases per x, x doesn’t change Vertical Reflection -if a < 0, then the function is reflected off the x axis Vertical Translation – y = ab^(x)+k -K dictates the vertical translation up or down -If K is positive, the entire translation is shifted up by the value of k -If K is negative, the entire translation is shifted down by the value of k Horizontal Translation -y = ab^(x+k) -K dictates the horizontal translation left and right -if K is negative, the function shifts right by the value of k – if K is positive, the function shifts left by the value of k -sometimes, the true translation/value of K be revealed if the horizontal stretch is factored Horizontal Stretch ● y = ab^p(x) ● P dictates the horizontal stretch and compression ● P should be factored out of the bracket ● If P > 1, then the function is compressed by the factor of 1/p ● If 0 > p > 1, then the function is stretched by the factor of 1/p ● Stretch factor is the reciprocal of what’s displayed in the equation Horizontal Reflection ● The value of P from horizontal stretching defines the reflection ● If it’s negative, the function will reflect off the Y axis.