Exponential Functions: Transformations Explained
Learn about exponential functions and their transformations, including key concepts such as coefficients, bases, exponents, and how altering these values affects the graph properties. Explore examples and understand how adjustments impact the y-intercept and overall function. Author: Culan O'Meara.
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Presentation Transcript
LCHL Strand 5 Functions: Transformations: Exponential Functions Culan O Meara Ballinrobe Community School
Functions: Key words Recap Variable: A symbol(often x,y,z) we use to describe a number we don t know the value of or where value can change Constant: A number that doesn t change e.g 11, -2, 54. Not attached to any variable. Exponent: Another word for power or order or index Coefficient: this is a number attached to a variable(normally in front) e.g. with the term 2x .2 is the coefficient of x Leading Coefficient: The coefficient of the highest power Y-intercept: Where the function crosses y-axis X-intercept: Where function crosses x-axis also called a Root Author: Culan O'Meara
Exponential Functions: Transformations An exponential function has three parts: Coefficient Base Exponent ? ? = ??? With Exponential functions, like with linear, quadratic and cubic, altering the values will change the properties of the graph in a specific way. Author: Culan O'Meara
Exponential Functions: Transformations With the example shown, the original function(in blue) is h ? = 2?. This can also be written as = 1.2? When we change the 2?coefficient, we can see that the new function ? ? = 3.2? (in red) has steepened Note that with exponential functions, the y-intercept is determined by the value of the coefficient However, as we see on next slide, adding in a constant will alter y-intercept further Author: Culan O'Meara
Exponential Functions: Transformations With the example shown, the original function(in blue) is h ? = 2?. This can also be written as = 1.2? When we change the constant(from 0), we can see that the new function ? ? = 2?+ 3 (in green) has moved up 3 units Author: Culan O'Meara
Exponential Functions: Transformations With the example shown, the original function(in blue) is h ? = 2?. When we change the exponent, we can see that the new function ? ? = 2?+2 (in pink) has steepened The y-intercept has changed to 4 This change gives same result as changing the coefficient to 4 or 22 due to Law 1 of Indices Author: Culan O'Meara
