#### Graphs of the exponential function.

1.
Sketch the graphs of the following functions:
1.1
y = 3x + 1  − 1
1.2
y = 3x − 1   + 2
1.3
y = 21 − x   + 3
1.4
y = 32 − x  − 3
1.5
y = 2.3x − 1   + 2
1.6
y = 3.21 − x   − 3
2.
The figures show the graphs of the functions with equation y = ax + p   + q. Use the information given
in the figure to detemine the values of p and q :
2.1 2.2 1
y = 2x + p  + q
y = (—)x + p  + q
3
B is the point (0 ; 1,5)
Horizontal asymptote: y = −3 and A (1 ; 0);
B is the point (0 ; 6) and P (2 ; −2)
2.3 2.4 1
y = 2x + p  + q
y = (—)x + p  + q
2
Given: A (3 ; 0), B(0 ; −1,75) and P(2 ; −1)
Given: B(0 ; 2,33) and P(−2 ; 5)
2.5 2.6 y = a.b  + q  and y = 1
y = a.b  + q
Given: A (1 ; 7) and B(0 ; 3)
Given: A(0 ; 0) and B(−2 ; 9)
3.
The figure shows the graph of y = 4x − 1   − 2 3.1
Calculate the intercepts on the axes.
3.2
Calculate the value of p if P(2 ; p) is a point on the graph.
3.3
Calculate the value of r if R(r ; &mins; 1) is a point on the graph.
3.4
Write down the domain of the function.
3.5
Write down the range of the function.
4.
The figure shows the graph of y = 2− x + 1   + 2 4.1
Calculate the intercepts on the axes.
4.2
Calculate the value of p if P(-1 ; p) is a point on the graph.
4.3
Calculate the value of r if R(r ; 2,25) is a point on the graph.
4.4
Write down the domain of the function.
4.5
Write down the range of the function.
4.6
The function h(x) is formed when the function above is
translated 4 units downwards. Write down the equation of the function h(x).
1
5.
The figure shows the graph of y =  ( —— ) x − 1   − 4
2 5.1
Calculate the intercepts on the axes.
5.2
Calculate the value of c if C(c ; 4) is a point on the graph.
5.3
Write down the domain of the function.
5.4
Write down the range of the function.
5.5
The function h(x) is formed when the function above is
translated 2 units upwards. Write down the equation of the function h(x).
1
6.
The figure shows the graph of y =  ( —— ) x + p   + q
3 6.1
Calculate the values of p and q.
6.2
Calculate the value of p if P(p ; 2) is a point on the graph.
6.3
Write down the domain of the function.
6.4
Write down the range of the function.
6.5
The function h(x) is formed when the function above is
translated 3 units upwards. Write down the equation of the function h(x).
6.6
Write down the coordinates of the Y-intercept of h(x).