Please help with this problem

Question

The point (19,4) is on the graph of y=f(x)

a)	A point on the graph of y=g(x), where g(x)=f(x−1) is
b)	A point on the graph of y=g(x) , where g(x)=f(x)−4 is
c)	A point on the graph of y=g(x) , where g(x)=−f(x) is
d)	A point on the graph of y=g(x) , where g(x)=9 f(x)is
e)	A point on the graph of y=g(x), where g(x)=14 f(x) is
f)	A point on the graph of y=g(x) , where g(x)=f(−x) is

Answer 1

Hi Latasha..

Your question has to do with transformation of functions.

The point (19,4) is on the graph of y=f(x)

a) A point on the graph of y=g(x), where g(x)=f(x−1) is

f(x-1) causes a horizontal shift of graph to the right

x becomes x+1

y stays y

(19,4) --> (20,4)

b) A point on the graph of y=g(x) , where g(x)=f(x)−4 is

f(x) - 4 causes a vertical shift of graph down 4

x --> x

y --> y-4

(19,4) --> (19,0)

c) A point on the graph of y=g(x) , where g(x)=−f(x) is

-f(x) causes a reflection across the x-axis

x --> x

y --> -y

(19,4) --> (19,-4)

d) A point on the graph of y=g(x) , where g(x)=9 f(x)is

9 f(x) causes a vertical stretch

x --> x

y --> 9y

(19,4) --> (19,36)

e) A point on the graph of y=g(x), where g(x)=14 f(x) is

14 f(x) causes a vertical stretch

x --> x

y --> 14y

(19,4) --> (19, 56)

f) A point on the graph of y=g(x) , where g(x)=f(−x) is

-f(x) causes a reflection across the y-axis

x --> -x

y --> y

(19,4) --> (-19,4)

Hope this helps

Let me know if you need more clarification :)