Since y=a^x is defined for all real values of x,we can sketch the graph y=a^(x ). However,if a is negative there are many values for x for which a^(x ) is undefined.For example
(-2)^(1/2)=√(-2.)
Consequently,functions y=a^x are defined only when a>0 (and a≠1)
There are two cases to consider a>1 and 0 Graphs of exponential functions can be obtained from the basic graph 〖y=a〗^x by means of translation, reflections and dilations. Using your knowledge of the transformations indicated, describe with the aid of sketches how the following could be obtained using the graph 3^x
a) 3^2x
b) 3^(x-2)+2
c) 1-3^(-x)
I don't understand this please help?
(-2)^(1/2)=√(-2.)
Consequently,functions y=a^x are defined only when a>0 (and a≠1)
There are two cases to consider a>1 and 0 Graphs of exponential functions can be obtained from the basic graph 〖y=a〗^x by means of translation, reflections and dilations. Using your knowledge of the transformations indicated, describe with the aid of sketches how the following could be obtained using the graph 3^x
a) 3^2x
b) 3^(x-2)+2
c) 1-3^(-x)
I don't understand this please help?
-
this is basic exponential function, as a function, they have some properties.
such as;
if f(x) is original function
-f(x) => reflect to x-axis
f(-x) => reflect to y axis
f(x) ± c => vertical shift up(+) or down(-) c units.
f(x±b) => horizontal shift left (+) or right (-) b units
f(ax) => if a>1, vertical stretch. if 0
now, we see what's happen.
f(x) = 3^x
a) 3^2x => f(ax) => if a>1, vertical stretch
b) 3^(x-2)+2 => horizontal shift right (-) b units and vertical shift up(+) c
c) 1-3^(-x) = -3^(-x)+1 => reflect to y axis, reflect to x-axis also, and vertical shift up(+)
such as;
if f(x) is original function
-f(x) => reflect to x-axis
f(-x) => reflect to y axis
f(x) ± c => vertical shift up(+) or down(-) c units.
f(x±b) => horizontal shift left (+) or right (-) b units
f(ax) => if a>1, vertical stretch. if 0
now, we see what's happen.
f(x) = 3^x
a) 3^2x => f(ax) => if a>1, vertical stretch
b) 3^(x-2)+2 => horizontal shift right (-) b units and vertical shift up(+) c
c) 1-3^(-x) = -3^(-x)+1 => reflect to y axis, reflect to x-axis also, and vertical shift up(+)