Math  /  Algebra

QuestionFor help with questions 5 to 8, refer to Investigate 2.
5. a) Copy the graph. b) \square b) Write an equation for this exponential function. c) c) Graph the line y=xy=x on the same grid. d) Sketch a graph of the inverse of the function by reflecting its graph in the line y=xy=x.

Studdy Solution
To sketch the inverse of the function, reflect the graph of the function across the line y=x y = x .
The inverse of an exponential function y=2x+1 y = 2^{x+1} is a logarithmic function. The inverse function can be expressed as: x=2y+1 x = 2^{y+1} Solving for y y , we get: y=log2(x)1 y = \log_2(x) - 1
Sketch this graph by reflecting the original graph across the line y=x y = x .
The equation of the exponential function is:
y=2x+1 y = 2^{x+1}
The inverse function is:
y=log2(x)1 y = \log_2(x) - 1

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